Question

How do you prove `1 - 2 sin^2r + sin^4r = cos^4r`?

Answer 1

Use the fact that `1+2x^2 +x^4` can be factored. It is a perfect square.

`1+2x^2 +x^4 = (1-x^2)^2`.

So,

`1-2sin^2r+sin^4r = (1-sin^2r)^2 = (cos^2 r )^2 = cos4r`