prove the identity!!!!!!!!!!!!

Question

sin^2 a*cos^2a=1/8(1-cos^4a)

Answer 1

Recall the formulas

sin^2 a =(1-cos2a)/2

cos^2 a =(1+cos2a)/2

sin^2 a*cos^2 a=(1-cos2a)/2*(1+cos2a)/2

                            =(1-cos^2 (2a))/4

Recall the formula

cos^2(2a)=(1+cos4a)/2

sin^2 a*cos^2 a=(1-((1+cos4a)/2)/4

                             =(1-cos4a)/8