What is expand ((1+sin(x))^2)/2 ?

The solution to expand ((1+sin(x))^2)/2 is 1/2+sin(x)+(sin^2(x))/2

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

expand

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

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

Solution steps

\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}

Apply the fraction rule:

\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}

Divide the numbers:

\frac{2}{2} = 1

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

\frac{5 z ^{2} ( z + 2 )}{3 z - 1}

\frac{s}{( s ^{2} + 2 s + 2 ) ( s + 1 )}

t^{5} e^{2 t} d (t - 2)

\frac{- 2 x + h}{( x ^{2} ) ( x + h ) ^{2}}

e^{t^{2}} (4 t^{3} - 7 t^{2} + 9 t)

What is expand ((1+sin(x))^2)/2 ?
The solution to expand ((1+sin(x))^2)/2 is 1/2+sin(x)+(sin^2(x))/2