Posted by mailon on Thursday, September 4, 2008 at 10:29pm.
Let x^2 = y
What you have written is equivalent to
1 - 2 sin y = cos y
which is not a correct identity.
It looks like you have put parentheses in the wrong places. The outside ones are unecessary.
A correct version would be
1 - 2 (sin x)^2 = cos 2x
That is one of the double-angle identities
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