Dreisatzrechnung

Vereinfachung von Themen

Prozentrechnung

Umrechnung von Einheiten

Summen- und Produktzeichen

Elementargeometrie

Funktionsfolgen

Unterschied In/Homogen

Basis, Basiswechsel

Abbildungsmatrizen

Funktionen bestimmen

Geraden und Ebenen

Gruppen

lineare abbildung 

quadratische ergänzung

Baustatik 1

Anfangswertprobleme :)

Differentialgleichungen

basis 

QR-Algorithmus

QR-Zerlegung

Cholesky-Zerlegung

Bild & Urbild

Zweigstromanalyse

Transistor als Thermometer

Investment

Teilfolgen

Epsilon Delta Kriterium

prinzip der virtuellen verrückung 

Linear Kombination

Folgen, Reihen und Potenzreihen

Flächenpressung

Arbeit 

Cholesky Zerlegung

Polynomfunktionen beschreiben

Zu Maß-und Integrationstheorie: Majorisierte Konvergenz

Teilchenphysik und Festkörperphysik

Orthogonaltrajektorien

test

Taylorreihen

Regel von de L'Hopital

Mathe

KRAFT

Grenzwert Funktion 

Folgenkriterium

ϵ-δ Kriterium 

Beweis Stetigkeit 

Wahrheitstabelle

2x2 Matrix

Matrix invertieren

Basiswechselsatz

Lineare Abbildunge 

Vorderrad fahradgabel lagerkräfte berechnen 

Spannungsregelung

Jordan Normal Form

Test

Induktion 

Jordan-Normalform

Ansatz der Störfunktion zur Bestimmung der Partikulären Lösung

Kurvenintegral

dlg mithilfe inhomogenen linearen system lösen

Inverse einer Matrix

Gleichmäßige Stetigkeit

addition

Regel von L´Hospital

Lineare Abbildungen

dimension eines Untervektorraumes bestimmen

Stationäre Stoffübertragung

Polplan, Prinzip der virtuellen Verrückungen

komplexe Ungleichungen 

Bidualräume

Dualräume

Taylorpolynome

Kern und Basis

Diagonalisieren einer Matrix

Rekursive Folgen

Exponentialreihe

Darstellungsmatrizen

restglied

Basiswechsel

Gamma Funktion

Newton Verfahren

Randwertaufgabe

Numerische Integration: Trapez- und Simpsonregel

Funktionenfolgen

dualräume

Dualraum

Komplexe Nullstellen

Chemie

Natascha Kirchmann

Differentialquotient

Folgedefinition des Funktionslimes

Grenzwerte und Stetigkeit 

Komplexe Zahlen

Kern und Bild 

Direkte Summe 

Koordinaten 

Exponentielle Verzinsung

Lineare Verzinsung

\[\begin{aligned} &amp;\left(\sin \frac{\pi}{4}+\sin \frac{\pi}{3}\right)\left(\sin \frac{\pi}{4}+\sin \frac{\pi}{6}\right)\left(\cos \frac{\pi}{4}-\cos \frac{\pi}{3}\right)\left(\cos \frac{\pi}{4}-\cos \frac{\pi}{6}\right) \\\\ &amp;=\left(\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\right) \end{aligned}\]

\[\begin{align} &amp;=\left(\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)\\\\
&amp;=\left(\frac{1}{2}-\frac{3}{4}\right)\left(\frac{1}{2}-\frac{1}{4}\right)\\\\
&amp;=-\frac{1}{4} \cdot \frac{1}{4}\\\\
&amp;=-\frac{1}{16} \end{align}\]

<mjx-container class="MathJax" jax="SVG" display="true" justify="left"><svg alt="\begin{align}
&=\left(\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)\\\\
&=\left(\frac{1}{2}-\frac{3}{4}\right)\left(\frac{1}{2}-\frac{1}{4}\right)\\\\
&=-\frac{1}{4} \cdot \frac{1}{4}\\\\
&=-\frac{1}{16}
\end{align}" style="vertical-align: -15.584ex;" xmlns="http://www.w3.org/2000/svg" width="57.632ex" height="32.299ex" role="img" focusable="false" viewBox="0 -7388 25473.3 14276" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-101-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-101-TEX-S4-28" d="M758 -1237T758 -1240T752 -1249H736Q718 -1249 717 -1248Q711 -1245 672 -1199Q237 -706 237 251T672 1700Q697 1730 716 1749Q718 1750 735 1750H752Q758 1744 758 1741Q758 1737 740 1713T689 1644T619 1537T540 1380T463 1176Q348 802 348 251Q348 -242 441 -599T744 -1218Q758 -1237 758 -1240Z"></path><path id="MJX-101-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-101-TEX-N-221A" d="M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z"></path><path id="MJX-101-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-101-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-101-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-101-TEX-S4-29" d="M33 1741Q33 1750 51 1750H60H65Q73 1750 81 1743T119 1700Q554 1207 554 251Q554 -707 119 -1199Q76 -1250 66 -1250Q65 -1250 62 -1250T56 -1249Q55 -1249 53 -1249T49 -1250Q33 -1250 33 -1239Q33 -1236 50 -1214T98 -1150T163 -1052T238 -910T311 -727Q443 -335 443 251Q443 402 436 532T405 831T339 1142T224 1438T50 1716Q33 1737 33 1741Z"></path><path id="MJX-101-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-101-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-101-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-101-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-101-TEX-N-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path id="MJX-101-TEX-N-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,5638.5)"><g data-mml-node="mtd"></g><g data-mml-node="mtd"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><use data-c="3D" xlink:href="#MJX-101-TEX-N-3D"></use></g><g data-mml-node="mrow" transform="translate(1333.6,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-101-TEX-S4-28"></use></g><g data-mml-node="mfrac" transform="translate(792,0)"><g data-mml-node="mn" transform="translate(646.5,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="msqrt" transform="translate(220,-920.5)"><g transform="translate(853,0)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(0,100.5)"><use data-c="221A" xlink:href="#MJX-101-TEX-N-221A"></use></g><rect width="500" height="60" x="853" y="840.5"></rect></g><rect width="1553" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(2807.2,0)"><use data-c="2B" xlink:href="#MJX-101-TEX-N-2B"></use></g><g data-mml-node="mfrac" transform="translate(3807.4,0)"><g data-mml-node="msqrt" transform="translate(220,676)"><g transform="translate(853,0)"><g data-mml-node="mn"><use data-c="33" xlink:href="#MJX-101-TEX-N-33"></use></g></g><g data-mml-node="mo" transform="translate(0,89)"><use data-c="221A" xlink:href="#MJX-101-TEX-N-221A"></use></g><rect width="500" height="60" x="853" y="829"></rect></g><g data-mml-node="mn" transform="translate(646.5,-686)"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g><rect width="1553" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(5600.4,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-101-TEX-S4-29"></use></g></g><g data-mml-node="mrow" transform="translate(7892.7,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-101-TEX-S4-28"></use></g><g data-mml-node="mfrac" transform="translate(792,0)"><g data-mml-node="mn" transform="translate(646.5,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="msqrt" transform="translate(220,-920.5)"><g transform="translate(853,0)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(0,100.5)"><use data-c="221A" xlink:href="#MJX-101-TEX-N-221A"></use></g><rect width="500" height="60" x="853" y="840.5"></rect></g><rect width="1553" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(2807.2,0)"><use data-c="2212" xlink:href="#MJX-101-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(3807.4,0)"><g data-mml-node="msqrt" transform="translate(220,676)"><g transform="translate(853,0)"><g data-mml-node="mn"><use data-c="33" xlink:href="#MJX-101-TEX-N-33"></use></g></g><g data-mml-node="mo" transform="translate(0,89)"><use data-c="221A" xlink:href="#MJX-101-TEX-N-221A"></use></g><rect width="500" height="60" x="853" y="829"></rect></g><g data-mml-node="mn" transform="translate(646.5,-686)"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g><rect width="1553" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(5600.4,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-101-TEX-S4-29"></use></g></g><g data-mml-node="mrow" transform="translate(14451.8,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-101-TEX-S3-28"></use></g><g data-mml-node="mfrac" transform="translate(736,0)"><g data-mml-node="mn" transform="translate(646.5,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="msqrt" transform="translate(220,-920.5)"><g transform="translate(853,0)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(0,100.5)"><use data-c="221A" xlink:href="#MJX-101-TEX-N-221A"></use></g><rect width="500" height="60" x="853" y="840.5"></rect></g><rect width="1553" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(2751.2,0)"><use data-c="2B" xlink:href="#MJX-101-TEX-N-2B"></use></g><g data-mml-node="mfrac" transform="translate(3751.4,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(4691.4,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-101-TEX-S3-29"></use></g></g><g data-mml-node="mrow" transform="translate(20045.9,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-101-TEX-S3-28"></use></g><g data-mml-node="mfrac" transform="translate(736,0)"><g data-mml-node="mn" transform="translate(646.5,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="msqrt" transform="translate(220,-920.5)"><g transform="translate(853,0)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(0,100.5)"><use data-c="221A" xlink:href="#MJX-101-TEX-N-221A"></use></g><rect width="500" height="60" x="853" y="840.5"></rect></g><rect width="1553" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(2751.2,0)"><use data-c="2212" xlink:href="#MJX-101-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(3751.4,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(4691.4,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-101-TEX-S3-29"></use></g></g></g></g><g data-mml-node="mtr" transform="translate(0,3339)"><g data-mml-node="mtd"></g></g><g data-mml-node="mtr" transform="translate(0,1339.5)"><g data-mml-node="mtd"></g><g data-mml-node="mtd"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><use data-c="3D" xlink:href="#MJX-101-TEX-N-3D"></use></g><g data-mml-node="mrow" transform="translate(1333.6,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-101-TEX-S3-28"></use></g><g data-mml-node="mfrac" transform="translate(736,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(1898.2,0)"><use data-c="2212" xlink:href="#MJX-101-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(2898.4,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="33" xlink:href="#MJX-101-TEX-N-33"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="34" xlink:href="#MJX-101-TEX-N-34"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3838.4,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-101-TEX-S3-29"></use></g></g><g data-mml-node="mrow" transform="translate(6074.7,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-101-TEX-S3-28"></use></g><g data-mml-node="mfrac" transform="translate(736,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="32" xlink:href="#MJX-101-TEX-N-32"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(1898.2,0)"><use data-c="2212" xlink:href="#MJX-101-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(2898.4,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="34" xlink:href="#MJX-101-TEX-N-34"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3838.4,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-101-TEX-S3-29"></use></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-660)"><g data-mml-node="mtd"></g></g><g data-mml-node="mtr" transform="translate(0,-2552)"><g data-mml-node="mtd"></g><g data-mml-node="mtd"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><use data-c="3D" xlink:href="#MJX-101-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(1333.6,0)"><use data-c="2212" xlink:href="#MJX-101-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(2111.6,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="34" xlink:href="#MJX-101-TEX-N-34"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3273.8,0)"><use data-c="22C5" xlink:href="#MJX-101-TEX-N-22C5"></use></g><g data-mml-node="mfrac" transform="translate(3774,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="34" xlink:href="#MJX-101-TEX-N-34"></use></g><rect width="700" height="60" x="120" y="220"></rect></g></g></g><g data-mml-node="mtr" transform="translate(0,-4288)"><g data-mml-node="mtd"></g></g><g data-mml-node="mtr" transform="translate(0,-6180)"><g data-mml-node="mtd"></g><g data-mml-node="mtd"><g data-mml-node="mi"></g><g data-mml-node="mo" transform="translate(277.8,0)"><use data-c="3D" xlink:href="#MJX-101-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(1333.6,0)"><use data-c="2212" xlink:href="#MJX-101-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(2111.6,0)"><g data-mml-node="mn" transform="translate(470,676)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use><use data-c="36" xlink:href="#MJX-101-TEX-N-36" transform="translate(500,0)"></use></g><rect width="1200" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg></mjx-container>

Vereinfachen Sie den Ausdruck \[\left(\sin \frac{\pi}{4}+\sin \frac{\pi}{3}\right)\left(\sin \frac{\pi}{4}+\sin \frac{\pi}{6}\right)\left(\cos \frac{\pi}{4}-\cos \frac{\pi}{3}\right)\left(\cos \frac{\pi}{4}-\cos \frac{\pi}{6}\right)\]

Vereinfachen Sie den Ausdruck <mjx-container class="MathJax" jax="SVG" display="true" justify="left"><svg alt="\left(\sin \frac{\pi}{4}+\sin \frac{\pi}{3}\right)\left(\sin \frac{\pi}{4}+\sin \frac{\pi}{6}\right)\left(\cos \frac{\pi}{4}-\cos \frac{\pi}{3}\right)\left(\cos \frac{\pi}{4}-\cos \frac{\pi}{6}\right)" style="vertical-align: -1.602ex;" xmlns="http://www.w3.org/2000/svg" width="67.518ex" height="4.202ex" role="img" focusable="false" viewBox="0 -1149.5 29843.1 1857.5" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-99-TEX-LO-28" d="M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z"></path><path id="MJX-99-TEX-N-73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path id="MJX-99-TEX-N-69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path id="MJX-99-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-99-TEX-N-2061" d=""></path><path id="MJX-99-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path id="MJX-99-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-99-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-99-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-99-TEX-LO-29" d="M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z"></path><path id="MJX-99-TEX-N-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"></path><path id="MJX-99-TEX-N-63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z"></path><path id="MJX-99-TEX-N-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path id="MJX-99-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mrow"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-99-TEX-LO-28"></use></g><g data-mml-node="mi" transform="translate(597,0)"><use data-c="73" xlink:href="#MJX-99-TEX-N-73"></use><use data-c="69" xlink:href="#MJX-99-TEX-N-69" transform="translate(394,0)"></use><use data-c="6E" xlink:href="#MJX-99-TEX-N-6E" transform="translate(672,0)"></use></g><g data-mml-node="mo" transform="translate(1825,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(1991.7,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="34" xlink:href="#MJX-99-TEX-N-34"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3223.9,0)"><use data-c="2B" xlink:href="#MJX-99-TEX-N-2B"></use></g><g data-mml-node="mi" transform="translate(4224.1,0)"><use data-c="73" xlink:href="#MJX-99-TEX-N-73"></use><use data-c="69" xlink:href="#MJX-99-TEX-N-69" transform="translate(394,0)"></use><use data-c="6E" xlink:href="#MJX-99-TEX-N-6E" transform="translate(672,0)"></use></g><g data-mml-node="mo" transform="translate(5452.1,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(5618.8,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="33" xlink:href="#MJX-99-TEX-N-33"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(6628.8,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-99-TEX-LO-29"></use></g></g><g data-mml-node="mrow" transform="translate(7392.4,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-99-TEX-LO-28"></use></g><g data-mml-node="mi" transform="translate(597,0)"><use data-c="73" xlink:href="#MJX-99-TEX-N-73"></use><use data-c="69" xlink:href="#MJX-99-TEX-N-69" transform="translate(394,0)"></use><use data-c="6E" xlink:href="#MJX-99-TEX-N-6E" transform="translate(672,0)"></use></g><g data-mml-node="mo" transform="translate(1825,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(1991.7,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="34" xlink:href="#MJX-99-TEX-N-34"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3223.9,0)"><use data-c="2B" xlink:href="#MJX-99-TEX-N-2B"></use></g><g data-mml-node="mi" transform="translate(4224.1,0)"><use data-c="73" xlink:href="#MJX-99-TEX-N-73"></use><use data-c="69" xlink:href="#MJX-99-TEX-N-69" transform="translate(394,0)"></use><use data-c="6E" xlink:href="#MJX-99-TEX-N-6E" transform="translate(672,0)"></use></g><g data-mml-node="mo" transform="translate(5452.1,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(5618.8,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="36" xlink:href="#MJX-99-TEX-N-36"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(6628.8,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-99-TEX-LO-29"></use></g></g><g data-mml-node="mrow" transform="translate(14784.9,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-99-TEX-LO-28"></use></g><g data-mml-node="mi" transform="translate(597,0)"><use data-c="63" xlink:href="#MJX-99-TEX-N-63"></use><use data-c="6F" xlink:href="#MJX-99-TEX-N-6F" transform="translate(444,0)"></use><use data-c="73" xlink:href="#MJX-99-TEX-N-73" transform="translate(944,0)"></use></g><g data-mml-node="mo" transform="translate(1935,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(2101.7,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="34" xlink:href="#MJX-99-TEX-N-34"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3333.9,0)"><use data-c="2212" xlink:href="#MJX-99-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(4334.1,0)"><use data-c="63" xlink:href="#MJX-99-TEX-N-63"></use><use data-c="6F" xlink:href="#MJX-99-TEX-N-6F" transform="translate(444,0)"></use><use data-c="73" xlink:href="#MJX-99-TEX-N-73" transform="translate(944,0)"></use></g><g data-mml-node="mo" transform="translate(5672.1,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(5838.8,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="33" xlink:href="#MJX-99-TEX-N-33"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(6848.8,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-99-TEX-LO-29"></use></g></g><g data-mml-node="mrow" transform="translate(22397.3,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-99-TEX-LO-28"></use></g><g data-mml-node="mi" transform="translate(597,0)"><use data-c="63" xlink:href="#MJX-99-TEX-N-63"></use><use data-c="6F" xlink:href="#MJX-99-TEX-N-6F" transform="translate(444,0)"></use><use data-c="73" xlink:href="#MJX-99-TEX-N-73" transform="translate(944,0)"></use></g><g data-mml-node="mo" transform="translate(1935,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(2101.7,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="34" xlink:href="#MJX-99-TEX-N-34"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3333.9,0)"><use data-c="2212" xlink:href="#MJX-99-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(4334.1,0)"><use data-c="63" xlink:href="#MJX-99-TEX-N-63"></use><use data-c="6F" xlink:href="#MJX-99-TEX-N-6F" transform="translate(444,0)"></use><use data-c="73" xlink:href="#MJX-99-TEX-N-73" transform="translate(944,0)"></use></g><g data-mml-node="mo" transform="translate(5672.1,0)"><use data-c="2061" xlink:href="#MJX-99-TEX-N-2061"></use></g><g data-mml-node="mfrac" transform="translate(5838.8,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D70B" xlink:href="#MJX-99-TEX-I-1D70B"></use></g><g data-mml-node="mn" transform="translate(255,-686)"><use data-c="36" xlink:href="#MJX-99-TEX-N-36"></use></g><rect width="770" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(6848.8,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-99-TEX-LO-29"></use></g></g></g></g></svg></mjx-container>

Dies ist eine interaktive Aufgabe zu: Vereinfachung von Themen mit praktischen Tipps zum Lösen und einer Zusammenfassung der nötigen Theorie

Grundlagen - Vereinfachung von Themen | Aufgabe mit Lösung

Aufgabenstellung:

Lösungsweg:

Lösung: