If tan(pi sin theta) = cot(pi cos theta), the | vedclass

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Question

$\frac{\sin (\pi \sin 	heta)}{\cos (\pi \sin 	heta)}=\frac{\cos (\pi \cos 	heta)}{\sin (\pi \cos 	heta)}$

$\Rightarrow \cos (\pi \cos 	heta+\p

Vedclass · Accepted Answer

$\frac{1}{{\sqrt 7 }}$

Vedclass · Answer

$\frac{\sin (\pi \sin 	heta)}{\cos (\pi \sin 	heta)}=\frac{\cos (\pi \cos 	heta)}{\sin (\pi \cos 	heta)}$

$\Rightarrow \cos (\pi \cos 	heta+\pi \sin 	heta)=0$

$\Rightarrow(\cos 	heta+\sin 	heta) \pi=\pm \frac{\pi}{2}$

$\Rightarrow \cos 	heta+\sin 	heta=\pm \frac{1}{2}$

$\Rightarrow \cos \left(	heta-\frac{\pi}{4}ight)=\pm \frac{1}{2 \sqrt{2}}$

$\Rightarrow \cot \left(	heta-\frac{\pi}{4}ight)=\pm \frac{1}{\sqrt{7}}$

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

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