Question

How do you use the double angle or half angle formulas to prove `cos(2x) = [cos(x)]^2 - [sin(x)]^2`?

Answer 1

Prove that cos 2x = (cos^2 x - sin^2 x)

Explanation:

Use the trig 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`