Question

Sin^8x - cos^8x = (sin^2 - cos^2x)(1-2sin^2xcos^2x)m

Answer 1

sin^8x - cos^8x = (sin^4x)^2 - ( cos^4x )^2

(sin^4 x- cos^4x)(sin^4 x+cos^4x)

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

(sin^2x- cos^2x ) [( sin^2x)^2 +(cos^2x)^ + 2sin^2x× cos^2 x- 2sin^2x × cos^2x]

(sin^2x- cos^2x ) [ ( sin^2 x+ cos^2x)^2 -2sin^2x× cos^2x]

(sin^2x - cos^2x)(1-2sin^2x× cos^2x)