Докажите тождество: sin^2x + sin^4x + cos^2x - cos^4x = 1 - cos2x

Question

Докажите тождество: sin^2x + sin^4x + cos^2x - cos^4x = 1 - cos2x

Answer 1

Sin²x+sin⁴x + cos²x - cos⁴x=1-cos2x
1-(cos⁴x-sin⁴x) = 1-cos2x
1-(cos²x-sin²x)(cos²x+sin²x) = 1-cos2x
1 - cos2x = 1- cos 2x