Question

Prove the identity
(sin^4)x - (cos^4)x = (sin^2)x - (cos^2)x

Answer 1

\[\sin ^{4}x - \cos ^{4}x = \sin ^{2}x - \cos ^{2}x\]

Answer 2

apply difference of squares to the left once, and look for an identity

Answer 3

sin^4x-cos^4x=(sin^2x+cos^2x )(sin^2x-cos^2x ).....(2)

(sin^2x+cos^2x )=1.................(1)

hence from 1 and 2

1((sin^2x-cos^2x )

Answer 4

why use a double-angle formula?
shivams' two-step answer is fine