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

\(\frac12(\frac14)(\frac54)\)

Please please please any help would be WONDERFUL

Guest Jul 25, 2020