Can you prove that cossquaredx - sinsquaredx equals 2cossquaredx -1?

Answer 1

3

Answer 2

When proving an identity, you may manipulate only one side of the equation throughout. You may not use normal algebraic techniques to manipulte both sides. Let's begin with the identity you wish to prove. cos2x - sin2x ?=? 2cos2x - 1 We know that sin2x + cos2x = 1 (Pythagorean Identity). Therefore, sin2x = 1 - cos2x. Substituting for sin2x, we may write cos2x - (1 - cos2x) ?=? 2cos2x - 1 cos2x - 1 + cos2x ?=? 2cos2x - 12cos2x -1 = 2cos2x - 1 The identity is proved. (Note that once the identity is proved, you may remove the question marks from around the equal sign.)