Question

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

Answer 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`