Question

How do you prove `cos^4theta-sin^4theta)=cos2theta`?

Answer 1

Prove trig identity

Explanation:

cos^4 x - sin^4 x = (cos^2 x - sin^2 x)(cos^2 + sin^2 x)
We know:
`cos^2 x + sin^2 x = 1`
`cos^2 x - sin^2x = cos 2x`
Therefor: `(cos^4 x- sin^4 x) = cos 2x`