Question

How do you prove `cos^4 p - sin^4 p = cos 2 p`?

Answer 1

Use the difference of squares formula and double angle identity:
`cos^2x - sin^2x = cos2x`

Explanation:

`cos^4p - sin^4p = (cos^2p + sin^2p)(cos^2p-sin^2p)`

`= 1(cos^2p-sin^2p)`

`=cos2p`