Question

How do you simplify `cos^4x-sin^4x`?

Answer 1

cos 2x

Explanation:

`f(x) = cos^4x - sin^4 x = (cos^2 x - sin^2 x)(cos^2 x + sin^2 x)`
Reminder of trig identities:
`cos^2 x - sin^2 x = cos 2x`
`(sin^2 x + cos^2 x) = 1`
Therefor,
`f(x) = cos 2x`