Solution
= Solution
For a smooth <exact differential form> $Mdx+Ndy$, its coefficients must satisfy $M_y=N_x$ by <Clairaut's theorem>. Here
$$
M_y=\sin x\cos y,\qquad N_x=-\sin x\cos y.
$$
These are not equal as <functions> on the plane, so \b[the form is not exact]. Equality at isolated points or along some lines is insufficient: an exactness test must hold throughout an open domain.