What is expand ((2+2cos(θ))^2)/2 ?

The solution to expand ((2+2cos(θ))^2)/2 is 2cos^2(θ)+4cos(θ)+2

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expand ((2+2cos(θ))^2)/2

expand

\frac{( 2 + 2 cos ( θ ) ) ^{2}}{2}

2 cos^{2} (θ) + 4 cos (θ) + 2

Solution steps

\frac{( 2 + 2 cos ( θ ) ) ^{2}}{2}

(2 + 2 cos (θ))^{2} = 4 + 8 cos (θ) + 4 cos^{2} (θ)

= \frac{4 + 8 cos ( θ ) + 4 cos ^{2} ( θ )}{2}

Factor

4 + 8 cos (θ) + 4 cos^{2} (θ) : 4 (1 + 2 cos (θ) + cos^{2} (θ))

= \frac{4 ( 1 + 2 cos ( θ ) + cos ^{2} ( θ ) )}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2 (cos^{2} (θ) + 2 cos (θ) + 1)

Distribute parentheses

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

Simplify

2 cos^{2} (θ) + 2 \cdot 2 cos (θ) + 2 \cdot 1 : 2 cos^{2} (θ) + 4 cos (θ) + 2

= 2 cos^{2} (θ) + 4 cos (θ) + 2

\frac{d}{d Y} ((i) (L i + L Y))

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

(- 0, 16 + 0.33 j) (0.1 + 0.1 j)

5 (q + 5) e^{\frac{- q + 5}{5}}

What is expand ((2+2cos(θ))^2)/2 ?
The solution to expand ((2+2cos(θ))^2)/2 is 2cos^2(θ)+4cos(θ)+2