Question

If $\tan \left(\pi \cos \theta \right)=\cot \left(\pi \sin \theta \right)$, then $\cos (\theta -\frac{\pi }{4})=$

Answer 1

Now,

$\tan \left(\pi \cos \theta \right)=\cot \left(\pi \sin \theta \right)$

or, $\tan \left(\pi \cos \theta \right)=\tan \{\frac{\pi }{2}-(\pi \sin \theta \left)\right\}$

or, $\pi \cos \theta =\frac{\pi }{2}-\pi \sin \theta$

or, $\cos \theta +\sin \theta =\frac{1}{2}$

or, $\frac{1}{\sqrt{2}}.\cos \theta +\frac{1}{\sqrt{2}}\sin \theta =\frac{1}{2\sqrt{2}}$

or, $\cos \frac{\pi }{4}.\cos \theta +\sin \frac{\pi }{4}.\sin \theta =\frac{1}{2\sqrt{2}}$

or, $\cos (\theta -\frac{\pi }{4})=\frac{1}{2\sqrt{2}}$