True-or-False :If $\tan(\pi \cos \theta)=\cot (\pi \sin \theta)$,then $\cos(\theta-\large\frac{\pi}{4})$$=\pm \large\frac{1}{2\sqrt 2}$

Question

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} $