Question

sin4 θ +2sin2 θ ·cos2 θ = 1 − cos4 θ

Answer 1

I am assuming that it is sin^4 theta and not sin 4theta and other terms also.

LHS

= sin^4 A + 2 sin^2 A cos^2 A

= sin^2 A ( sin^2 A + 2 cos^2 A)

= sin^2 A ( sin^2 A + cos^2 A + cos^2A)

= sin^2 A ( 1 + cos^2 A)

= (1 - cos^2 A) (1 + cos^2 A)

= 1 - cos^4 A

RHS proved