Question

How to prove `sin^2 theta - cos^2 theta = 1 -2cos^2 theta` ?

Answer 1

See answer below

Explanation:

Given: Prove `sin^2 theta - cos^2 theta = 1 - 2 cos^2 theta`

Use the Pythagorean Identity: `" "sin^2 theta+ cos^2 theta = 1`

Rearrange the identity: `" "sin^2 theta = 1 - cos^2 theta`

Start with the left side of the equation and substitute the rearranged identity:

`sin^2 theta - cos^2 theta = 1 - cos^2 theta - cos^2 theta`

Combine like-terms:

`= 1 - 2 cos^2 theta` This is the right-side

Q.E.D.