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# Super Small Question

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I have already solved most of this problem and I am just on the last part where i have a small question.

The question:

If $$\sin (\pi \cos x) = \cos (\pi \sin x),$$ enter all possible values of $$\sin 2x$$ separated by commas.

I know that the only time that $$\pi\sin(x)$$ and $$\pi\cos(x)$$ are equal is when $$\pi\sin(x)$$and $$\pi\cos(x)$$ are equal to pi/4 and 5pi/4.

That means sin(x)=1/4 or 5/4 and that cos(x)=1/4 or 5/4.

If we use double angle formula sin2x=2sinxcosx. we can just plug in sinx and cosx.

THIS IS THE PART I HAVE TROUBLE WITH

Are the solutions

$$\frac12(\frac14)(\frac14)$$

$$\frac12(\frac54)(\frac54)$$

OR do the solutions also include

$$​​​​\frac12(\frac14)(\frac54)$$