Use the Pythagorean identity to show that the double angle formula for cosine can be written as

Question

a) cos2x = 1 - 2sin^2x
b) cos2x = 2cos^2x - 1

Answer 1

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