Question

How do you prove that cos^4x-sin^4x=cos(2x) ?

Answer 1

`f(x) = cos^4 x - 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`
`cos^2 x + sin^2 x = 1`
Therefor,
f(x) = cos 2x. Proved.