Prove the identity

Question

Cos²x - sin²x = 2cos²x - 1

Answer 1

To prove the identity, we will start with the left side of the equation and manipulate it until we obtain the right side.

Starting with the left side:
cos²x - sin²x

Using the Pythagorean identity:
cos²x - (1 - cos²x)

Expanding the expression:
cos²x - 1 + cos²x

Combine like terms:
2cos²x - 1

Therefore, the left side (cos²x - sin²x) can be simplified to the right side (2cos²x - 1).