erweitern ((1-cos(6x))^2)/4

Lösung

erweitern

\frac{( 1 - cos ( 6 x ) ) ^{2}}{4}

\frac{1}{4} - \frac{cos ( 6 x )}{2} + \frac{cos ^{2} ( 6 x )}{4}

Schritte zur Lösung

\frac{( 1 - cos ( 6 x ) ) ^{2}}{4}

(1 - cos (6 x))^{2} = 1 - 2 cos (6 x) + cos^{2} (6 x)

= \frac{1 - 2 cos ( 6 x ) + cos ^{2} ( 6 x )}{4}

Wende Bruchregel an:

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

\frac{1 - 2 cos ( 6 x ) + cos ^{2} ( 6 x )}{4} = \frac{1}{4} - \frac{2 cos ( 6 x )}{4} + \frac{cos ^{2} ( 6 x )}{4}

= \frac{1}{4} - \frac{2 cos ( 6 x )}{4} + \frac{cos ^{2} ( 6 x )}{4}

Streiche

\frac{2 cos ( 6 x )}{4} : \frac{cos ( 6 x )}{2}

= \frac{1}{4} - \frac{cos ( 6 x )}{2} + \frac{cos ^{2} ( 6 x )}{4}

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e x p an d 5 i

e x p an d \frac{x}{( x + 6 ) ( x - 1 )}

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

e x p an d \frac{x ^{3} + 5 x ^{2} + 3}{s ^{2} ( s ^{2} - 3 s - 18 )}