How do you prove cos(3x)= 4cos^3(x)-3cos(x) using the double angle identity?

1 Answer
Aug 15, 2015

It's all about trigonometry (duh)

Explanation:

LHS
= cos 3x
= cos (x + 2x)
= cos x cos 2x - sin x sin 2x [note cos 2x and sin 2x]
= cos x (2 cos^2 x - 1) - sin x (2 sin x cos x) [open the brackets]
= 2 cos^3 x - cos x - 2 sin^2 x cos x
= 2 cos^3 x - cos x - 2 (1 - cos^2 x) cos x [sin^2 x + cos^2 x = 1]
= 2 cos^3 x - cos x - 2 (cos x - cos^3 x) [open the brackets]
= 2 cos^3 x - cos x - 2 cos x + 2 cos^3 x
= 4 cos^3 x - 3 cos x [collect terms]
= RHS