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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

cos (3 x)

Rewrite using trig identities

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

Factor

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

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

(sec (x) - 1) (sec (x) + 1) \cdot cot^{2} (x) = 1

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

tan^{2} (x) + tan (x) cot (x) = sec^{2} (x)

cos (4 θ) = 2 (cos (2 θ))^{2} - 1

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

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