how can i solve cos^2-sin^2=2cos-1

Question

im not sure which identities to use and how to prove it.

Answer 1

Solve: cos^2(θ) - sin^2(θ) = 2cos(θ) - 1

cos^2(θ) + sin^2(θ) = 1 [Pythagorean Identity]

sin^2(θ) = 1 - cos^2(θ)

Substitute in equation to solve:

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

2cos^2(θ) - 1 = 2cos(θ) - 1

2cos^2(θ) = 2cos(θ)

cos^2(θ) – cos(θ) = 0

cos(θ)(cos(θ) – 1) = 0

Use Zero Product Property:

cos(θ) = 0 or cos(θ) = 1

θ = pi/2 + 2n pi, n integer

θ = 3 pi/2 + 2n pi, n integer

θ = 0 + 2n pi, n integer

Answer 2

You need to put complete question; you missed to in lure the variable x's in your question. 

 

The most common trig identity is sin^2(x) + cos^2(x) = 1. Try using that.