Докажите тождество: sin^4 α-cos^4 α= -cos2α

Question

Докажите тождество:
sin^4 α-cos^4 α= -cos2α

Answer 1

(1-cos2alpha)^2/4-(1+cos2alpha)^2/4 = -cos2alpha
(1-cos2alpha-1-cos2alpha)(1-cos2alpha+1+cos2alpha)/4 = -cos2alpha
-2cos2alpha*2/4 = -cos2alpha
-cos2alpha == -cos2alpha