erweitern (1-cos(7x))/((sin(5x))^2)

Lösung

erweitern

\frac{1 - cos ( 7 x )}{( sin ( 5 x ) ) ^{2}}

\frac{1}{sin ^{2} ( 5 x )} - \frac{cos ( 7 x )}{sin ^{2} ( 5 x )}

Schritte zur Lösung

\frac{1 - cos ( 7 x )}{sin ^{2} ( 5 x )}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 - cos ( 7 x )}{sin ^{2} ( 5 x )} = \frac{1}{sin ^{2} ( 5 x )} - \frac{cos ( 7 x )}{sin ^{2} ( 5 x )}

= \frac{1}{sin ^{2} ( 5 x )} - \frac{cos ( 7 x )}{sin ^{2} ( 5 x )}

s im pl i f y \frac{1}{2} (x - \frac{1}{2} sin (2 x)) cos (x)

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

e x p an d \frac{( e ^{x} + e ^{- x} ) ^{2}}{4}

e x p an d \frac{8 x - 5}{( 4 x - 7 ) ^{2}}

e x p an d (\frac{4}{2 - 5 x})^{3}