Is 2(cos(3θ)+3cos(θ))=(2cos(θ))^3 ?

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

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prove 2(cos(3θ)+3cos(θ))=(2cos(θ))^3

prove

2 (cos (3 θ) + 3 cos (θ)) = (2 cos (θ))^{3}

True

Solution steps

2 (cos (3 θ) + 3 cos (θ)) = (2 cos (θ))^{3}

Manipulating left side

2 (cos (3 θ) + 3 cos (θ))

Rewrite using trig identities

= 8 cos^{3} (θ)

Manipulating right side

(2 cos (θ))^{3}

Simplify

(2 cos (θ))^{3} : 8 cos^{3} (θ)

= 8 cos^{3} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

tan (x) = tan (x) csc^{2} (x) + cot (- x)

tan (8 x) = \frac{2 tan ( x )}{1 - tan ^{2} ( x )}

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

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