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

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Answer 1 · 2015-05-21T03:26:35

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,

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

How do you prove 1 - 2 sin^2r + sin^4r = cos^4r1 - 2 sin^2r + sin^4r = cos^4r?