Prove the identity?

Question

cos^2-sin^2=2cos^2-1

Thanks for your help!

Answer 1

We know cos^2 + sin^2 = 1.

If we subtract 2cos^2 from both sides of the equation you're trying to prove we get -cos^2-sin^2=-1. Multiply through by -1 and you get cos^2 + sin^2 = 1.

Answer 2

Prove cos²x - sin²x = 2cos²x - 1

given
sin²x + cos²x = 1
therefore, sin²x = 1 - cos²x

cos²x - sin²x = 2cos²x - 1
cos²x - (1 - cos²x) = 2cos²x - 1
2cos²x - 1 = 2cos²x - 1

qed
.