Pre Calc
posted by John .
How to prove tan4x = 18 sin squared of cos squared of x

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?
Let's see.
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))