Question

Prove this idenity?
cos6x=2cos(squared)3x -1

Answer 1

Explanation:

cos6x=cos(3x+3x)=cos(3x)cos(3x) - sin (3x)sin(3x)= cos^2 (3x)- sin^2 (3x)= cos^2 (3x)- 1 + cos^2 (3x)= 2cos^2 (3x) -1

Answer 2

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 getcos^2(3x)−(1−cos^2(3x)) finally gathering like terms you get 2cos^2(3x)−1