Question

Use an angle sum identity to verify the identity .
cos 2 0 = 2 cos^2 0 - 1

Answer 1

Instead of theta, I will use x. Same proof, just easier variable to type, x.

cos (2x) = cos(x+x) = cos x cos x - sinx sin x
using the sum formula for cosine.

so, cos (2x) = cos^2x - sin^2x.
Now, since by a Pytahgoren Identity, sin^2x = 1 - cos^2x, substitute this in previous equation, so get

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

Done.