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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

\frac{2 ( 3 - 6 )}{3}

(1 + \frac{π}{2}) (π - \frac{π}{2})

2 (22500 ln (1968300000000) - 200)

\frac{( 4 - x ^{2} ) ^{3}}{8 x ^{3}}

\frac{d ^{2}}{d x ^{2}} ((y) (- 6 x^{4} + 9))

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