Question

Simplify the expression (1-2sin^2 θ)^2 + 4sin^2 θcos ^2 θ

Answer 1

we can do a substitution
cos(2t) = 1 - 2sin^2(t)

Answer 2

and
sin(2t) = 2 sin t cos t

Answer 3

(1-2sin^2 t)^2 + 4sin^2 t cos ^2 t
=(cos 2t) ^2 + (2 sin t cos t ) ^2
=(cos 2t ) ^2 + ( sin 2t ) ^2

can you simplify it now?

Answer 4

yes
thanks.