How do you prove cos2x = 2cos^2x -1?

Use the identity: cos (a + b) = cos a.cos b – sin a.sin b
##cos 2x = cos (x + x) = cos x.cos x – sin x. sin x = cos^2 x – sin^2 x ##=
##= cos^2 x – (1 – cos^2 x) = 2cos ^2 x – 1 ##