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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

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

\frac{2 x + 4}{( x - 1 ) ( x + 3 )}

2.856 \cdot 1 0^{7}

\frac{5 ( x - 10 )}{2}

P (4, - 1) y Q (- 2, 5)

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