erweitern ((1+sin(x))^2)/2

Lösung

erweitern

\frac{( 1 + sin ( x ) ) ^{2}}{2}

\frac{1}{2} + sin (x) + \frac{sin ^{2} ( x )}{2}

Schritte zur Lösung

\frac{( 1 + sin ( x ) ) ^{2}}{2}

(1 + sin (x))^{2} = 1 + 2 sin (x) + sin^{2} (x)

= \frac{1 + 2 sin ( x ) + sin ^{2} ( x )}{2}

Wende Bruchregel an:

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

\frac{1 + 2 sin ( x ) + sin ^{2} ( x )}{2} = \frac{1}{2} + \frac{2 sin ( x )}{2} + \frac{sin ^{2} ( x )}{2}

= \frac{1}{2} + \frac{2 sin ( x )}{2} + \frac{sin ^{2} ( x )}{2}

Teile die Zahlen:

\frac{2}{2} = 1

= \frac{1}{2} + sin (x) + \frac{sin ^{2} ( x )}{2}

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

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

e x p an d t^{5} e^{2 t} d (t - 2)

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

e x p an d e^{t^{2}} (4 t^{3} - 7 t^{2} + 9 t)