Prove the identity equation

Question

Prove the identity: Cos²'θ − Sin'²θ = 2Cos'²θ − 1

(using the fact that Sin²'θ + Cos²'θ = 1)

Answer 1

sin^2(x) + cos^2(x) = 1

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

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

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