Question

Prove that `cos 3x = 4cos^3 x - 3cos x` ?

Answer 1

Prove `cos 3x = 4cos^3 x - 3cos x`

Explanation:

Apply the trig identities:

• `cos (a + b) = cos a * cos b - sin a * sin b`
• `cos 2x = 2cos^2 x - 1`
• `sin 2x = 2sin x * cos x`

We get:

`cos 3x = cos (x + 2x) = cos x * cos 2x - sin x * sin 2x`

`= cos x(2cos^2 x - 1) - 2sin^2 x * cos x`

`= 2cos^3 x - cos x - 2cos x(1 - cos^2 x)`

`= 2cos^3 x - cos x - 2cos x + 2cos^3 x`

So

`cos 3x = 4cos^3 x - 3cos x`