Question

verify 1-sin^2(2x)=(1-2sin^2(x))^2

Answer 1

\[
1-\sin^2(2x)
\]Use the fact that \(\sin^2(y) + \cos^2(y) = 1\).
If we let \(y=2x\) then we would say \(\sin^2(2x) + \cos^2(2x) = 1\).\[
[\sin^2(2x) + \cos^2(2x)]-\sin^2(2x) = \cos^2(2x)
\]

Answer 2

Then there is a double angle formula: \[
\cos(2x) = 1-2\sin^2(x)
\]