Is (cos(θ)+cos(3θ))/(2cos(2θ))=cos(θ) ?

The answer to whether (cos(θ)+cos(3θ))/(2cos(2θ))=cos(θ) is True

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prove (cos(θ)+cos(3θ))/(2cos(2θ))=cos(θ)

prove

\frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( 2 θ )} = cos (θ)

True

Solution steps

\frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( 2 θ )} = cos (θ)

Manipulating left side

\frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( 2 θ )}

Rewrite using trig identities

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

tan^{3} (θ) = tan (θ) sec^{2} (θ) - tan (θ)

sin^{2} (θ) + sin (θ) = 1

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

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

sin (θ - \frac{3 π}{2}) = cos (θ)

Is (cos(θ)+cos(3θ))/(2cos(2θ))=cos(θ) ?
The answer to whether (cos(θ)+cos(3θ))/(2cos(2θ))=cos(θ) is True