Question

Докажите тождество 
sin^4a-cos^4a= - cos2a

Answer 1

$sin^{4} alpha -cos^{4} alpha =(sin^{2} alpha -cos^{2} alpha )(sin^{2} alpha +cos^{2} alpha )= \ (sin^{2} alpha -cos^{2} alpha )*1=-(cos^{2} alpha- sin^{2} alpha )=-cos^{2} alpha$