If $\tan (\pi \cos \theta) =\cot (\pi \sin \theta) $ then find the value of $\cos\left (\theta -\frac{\pi}{4}\right)$ If $\tan (\pi \cos \theta) =\cot (\pi \sin \theta) $ then find the value of $\cos \left(\theta -\frac{\pi}{4}\right).$
I could not get any idea to solve.  However I tried by using $\theta =0^\circ $. But could not get the answer. 

Hint -
$\tan (\pi \cos \theta) =\cot (\pi \sin \theta)$
$\tan(\pi \cos \theta) =\tan (\frac{\pi}2 - \pi \sin \theta)$
$\pi \cos \theta =\frac{\pi}2 - \pi \sin \theta$
$\cos \theta = \frac 12 - \sin \theta$
$\sin \theta + \cos \theta = \frac 12$
Now we have,
$\cos\left(\theta-\frac{\pi}{4}\right)$
$= \cos\theta \cos \frac{\pi}4 +\sin\theta \sin \frac{\pi}4$
$= \cos\theta \frac 1{\sqrt{2}} + \sin\theta \frac 1{\sqrt{2}}$
$= \frac1{\sqrt 2} \left( \cos\theta +\sin\theta \right)$
$ = \frac 1{\sqrt2} \left(\frac 12\right)$
$= \frac 1{2\sqrt2}$
