Is cos^2(θ)=(1+cos(2θ))/2 ?

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

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prove cos^2(θ)=(1+cos(2θ))/2

prove

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

True

Solution steps

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

Manipulating right side

\frac{1 + cos ( 2 θ )}{2}

Rewrite using trig identities

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cos ^{2} ( α )}{1 - sin ( α )} = 1 + sin (α)

2 sin^{2} (θ) - 1 = 1 - 2 cos^{2} (θ)

cos (θ - π) = - cos (θ)

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

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