erweitern cos(3(2t-pi/6))u(2t-pi/6)

Lösung

erweitern

cos (3 (2 t - \frac{π}{6})) u (2 t - \frac{π}{6})

2 t u cos (6 t - \frac{π}{2}) - \frac{π u cos ( 6 t - \frac{π}{2} )}{6}

Schritte zur Lösung

cos (3 (2 t - \frac{π}{6})) u (2 t - \frac{π}{6})

= u cos (3 (2 t - \frac{π}{6})) (2 t - \frac{π}{6})

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = cos (3 (2 t - \frac{π}{6})) u, b = 2 t, c = \frac{π}{6}

= cos (3 (2 t - \frac{π}{6})) u \cdot 2 t - cos (3 (2 t - \frac{π}{6})) u \frac{π}{6}

= 2 t u cos (3 (2 t - \frac{π}{6})) - \frac{π}{6} u cos (3 (2 t - \frac{π}{6}))

Vereinfache

2 t u cos (3 (2 t - \frac{π}{6})) - \frac{π}{6} u cos (3 (2 t - \frac{π}{6})) : 2 t u cos (6 t - \frac{π}{2}) - \frac{π u cos ( 6 t - \frac{π}{2} )}{6}

= 2 t u cos (6 t - \frac{π}{2}) - \frac{π u cos ( 6 t - \frac{π}{2} )}{6}

e x p an d \frac{( x + y ) ^{3}}{3}

e x p an d 9 n^{2} + 2 n^{2} \cdot 4 + 5 n^{2}

e x p an d \frac{( x - 1 ) ^{2}}{1 + x ^{2}}

e x p an d \frac{x}{( 1 + x ) ^{3}}

e x p an d \frac{2 x ^{3} + 5 x - 1}{( 5 x + 1 ) ^{3} ( x ^{2} + 9 ) ^{2}}