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

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

\frac{1 + cos ( 2 θ )}{2}

Use the Double Angle identity:

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

= \frac{1 + 2 cos ^{2} ( θ ) - 1}{2}

Simplify

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

\frac{1 + 2 cos ^{2} ( θ ) - 1}{2}

1 + 2 cos^{2} (θ) - 1 = 2 cos^{2} (θ)

1 + 2 cos^{2} (θ) - 1

Group like terms

= 2 cos^{2} (θ) + 1 - 1

1 - 1 = 0

= 2 cos^{2} (θ)

= \frac{2 cos ^{2} ( θ )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos^{2} (θ)

= cos^{2} (θ)

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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