Rewrite with only sin x and cos x. sin 2x - cos 2x

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Rewrite with only sin x and cos x. sin 2x - cos 2x

Mathematics
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This is so confusing because I know that what I did was correct, but my answer is not one of the choices.
well what do you know about sin(2x) and cos(2x)
So I kind of made the choices as the guide, so here's what I did.

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Other answers:

\[\sin2x-\cos2x\] \[2 \sin x \cos x-(1-2\sin^2x)\] \[2 \sin x \cos x -1+2\sin^2x\]
Here are the choices btw. a.2 sinx cosx - 1 + 2 sin2x b. 2 sin x cos2x - 1 + 2 sin2x c. 2 sin x cos2x - sin x + 1 - 2 sin2x d. 2 sin x cos2x - 1 - 2 sin2x And my answer is A.
that works.... so looking at the answer options they have used cos(2x) = 1 - 2 sin^2(x) so as you have posted 2sin(x)cos(x) - (1 - 2sin^2(x)) = 2 sin(x)cos(x) -1+ 2sin^2(x)
I know that sin^2x = 2 sin x cos x cos 2x = 1-2sin^2x = 2 cos^2x-1 =cos^2x-sin^2x
you have the correct solution
So am I correct?
Oh okay thanks! :)
yes \[2\sin(x)\cos(x) - 1 + 2 \sin^2(x)\]

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