Question 602425
sin^4 - cos^4 = 2sin^2 - 1


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


(sin^2-cos^2)(sin^2+cos^2) = 2sin^2 - 1


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


sin^2-cos^2 = 2sin^2 - 1


sin^2 - (1 - sin^2) = 2sin^2 - 1


sin^2 - 1 + sin^2 = 2sin^2 - 1


2sin^2 - 1 = 2sin^2 - 1


So this verifies the identity.