Is cos^2(x/2)= 1/2+1/2 cos(x) ?

The answer to whether cos^2(x/2)= 1/2+1/2 cos(x) is True

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prove cos^2(x/2)= 1/2+1/2 cos(x)

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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sin^{2} (θ) + (\frac{1}{2})^{2} = 1

(csc^{2} (x) - 1) sin (x) = cos^{2} (csc (x))

sin (θ) (cot (θ) + tan (θ)) = tan (θ)

Is cos^2(x/2)= 1/2+1/2 cos(x) ?
The answer to whether cos^2(x/2)= 1/2+1/2 cos(x) is True