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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (3 B)

Rewrite using trig identities

= 4 cos^{3} (B) - 3 cos (B)

Factor

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

= (- 3 + 4 cos^{2} (B)) cos (B)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

sin (θ + \frac{π}{2}) = cos (θ)

sin (2 x) = \frac{2 cot ( x )}{csc ^{2} ( x )}

(1 - cos (x)) (1 + sec (x)) = sec (x) - cos (x)

6 sin (5 π - x) = 6 sin (x)

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