I don't think you really meant
tan(4x) = 1 - sin^2(cos^2(x)), so do you mean
tan 4x = 1 - 8 sin^2 x cos^2 x?
8sin^2 x cos^2 x = 2*sin^2(2x))
tan(4x) =? 1 - 2sin^2(2x)
Naah. Check your problem again.
However, cos(4x) = 1 - 2sin^2(2x))
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