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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Factor

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

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

Rewrite using trig identities

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (\frac{θ}{2}) = \frac{1 - cos ( θ )}{sin ( θ )}

cot (\frac{1}{x}) = \frac{cos ( \frac{1}{x} )}{sin ( \frac{1}{x} )}

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

\frac{1}{2 cos ( x ) sin ( x )} = csc (2 x)

cos (x + \frac{π}{2}) = sin (x)

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