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No.

Remember: sin2 + cos2 = 1

So, in place of (1 - 2 sin2) we can write (sin2 + cos2 - 2 sin2).

Massage that around slightly: (sin2 + cos2 - 2 sin2) = cos2 - sin2

That's not equal to (sin2 - cos2), which is the original question we were asked.

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