What is expand ((1+cos(θ))^2)/2 ?

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

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expand ((1+cos(θ))^2)/2

expand

\frac{( 1 + cos ( θ ) ) ^{2}}{2}

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

Solution steps

\frac{( 1 + cos ( θ ) ) ^{2}}{2}

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

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\frac{( x - 6 ) ( x + 1 )}{( x - 3 )}

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\frac{x ^{2} - 6 x + 5}{( x - 3 ) ^{2}}

(3 x - \frac{1}{y})^{4}

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