4 sin^2 2 α-8 sin^4 α+8 sin^2 α

Question

4 sin^2 2 α-8 sin^4 α+8 sin^2 α

Answer 1

4sin²2α-8sin⁴α+8sin²α=4sin²2α-8sin²α*(sin²α-1)=4sin²2α-8sin²α*(-cos²α)=
=4sin²2α+8sin²α*cos²α=4sin²2α+2*(2sinα*cosα)²=4sin²2α+2sin²2α=6sin²2α