Is cos(3θ)=cos(θ)(cos^2(θ)-3sin^2(θ)) ?

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

Popular >

prove cos(3θ)=cos(θ)(cos^2(θ)-3sin^2(θ))

prove

cos (3 θ) = cos (θ) (cos^{2} (θ) - 3 sin^{2} (θ))

True

Solution steps

cos (3 θ) = cos (θ) (cos^{2} (θ) - 3 sin^{2} (θ))

Manipulating left side

cos (3 θ)

Rewrite using trig identities

= 4 cos^{3} (θ) - 3 cos (θ)

Factor

- 3 cos (θ) + 4 cos^{3} (θ) : cos (θ) (- 3 + 4 cos^{2} (θ))

= (- 3 + 4 cos^{2} (θ)) cos (θ)

Rewrite using trig identities

= cos (θ) (cos^{2} (θ) - 3 sin^{2} (θ))

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( θ )}{1 + sec ( θ )} = - cot (θ) + csc (θ)

cos (θ) = sec (θ) - (sin (θ)) (tan (θ))

cos (2 x - 90) = 2 sin (x) cos (x)

sin^{4} (x) - 2 sin^{2} (x) = cos^{4} (x) - 1

cot^{4} (a) = \frac{cos ^{4} ( a )}{sin ^{4} ( a )}

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