Is cos^4(θ)= 1/4+(cos(2θ))/2+(cos^2(2θ))/4 ?

The answer to whether cos^4(θ)= 1/4+(cos(2θ))/2+(cos^2(2θ))/4 is True

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prove cos^4(θ)= 1/4+(cos(2θ))/2+(cos^2(2θ))/4

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

= cos^{4} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

csc (u) = 2

\frac{csc ( x )}{cot ( x )} = csc (x) tan (x)

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

sin (x) + tan (x) = \frac{cos ( x )}{1 - sin ( x )}

Is cos^4(θ)= 1/4+(cos(2θ))/2+(cos^2(2θ))/4 ?
The answer to whether cos^4(θ)= 1/4+(cos(2θ))/2+(cos^2(2θ))/4 is True