Question

Buktikan cos^4alfa(1+tan^4alfa) = 1-2 sin^2alfa cos^2alfa

Answer 1

Cos^4 a( 1+tan^4 a)
cos^4 a(1+(sin^4a/cos^4 a)
=cos^4 a+sin^4 a
=(cos^2 a+sin^2 a)^2 -2sin^2 a.cos^2 a
=1-2.sin^2 a.cos^2 a