prove the following identity

Question

cos^4X - sin^4X = 1-2sin^2X

Answer 1

LS = (cos^2x + sin^2x)(cos^2x - sin^2x)
= 1((1-sin^2x) - sin^2x)
= 1 - 2sin^2x
= RS

Answer 2

Factorize the left hand side using:
A²-B²=(A+B)(A-B)
or
A⁴-B⁴ = (A²+B²)(A²-B²)