Solution
= Solution
Here $\sin^2x=(1-\cos2x)/2$ belongs to the <image>. Matching the two coefficients using $L(A+B\cos2x)=B\pi/2+A\pi\cos2x$ gives $A=-1/(2\pi)$, $B=1/\pi$. Consequently
$$
\boxed{y(x)=\frac{\cos2x-1/2}{\pi}+z(x),\qquad z\perp1,\quad z\perp\cos2x.}
$$
There are \b[infinitely many solutions], since any element of the infinite-dimensional <kernel> may be added.