Prove this idenity?

cos6x=2cos (squared) 3x - 1

cos (6x) = cos (2 (3x)) = cos (3x) + cos (3x)

applying the sum of angles formula for cosine you get

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

now by the Pythagorean identity for sine and cosine you get cos^2 (3x) - (1 - cos^2 (3x)) finally gathering like terms you get 2 cos^2 (3x) - 1