Докажите тождество sin^4 a-cos^4 a=sin^2 a-cos^2 a

Question

Докажите тождество sin^4 a-cos^4 a=sin^2 a-cos^2 a

Answer 1

A^2-b^2 = (a-b) (a+b)
sin^2a+cos^2a=1
(sin^2-cos^2a)(sin^a+cos^2a) = sin^2a-cos^2a
1(sin^2a-cos^2a) = sin^2a-cos^2a
sin^2a-cos^2a=sin^2a-cos^2a