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

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Question

(A) Given,$	an (\pi \cos 	heta)=\cot (\pi \sin 	heta)$ $\Rightarrow 	an (\pi \cos 	heta)=	an \left(\frac{\pi}{2}-\pi \sin 	hetaight)$ $\Right

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$\frac{1}{2 \sqrt{2}}$

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(A) Given,$	an (\pi \cos 	heta)=\cot (\pi \sin 	heta)$ $\Rightarrow 	an (\pi \cos 	heta)=	an \left(\frac{\pi}{2}-\pi \sin 	hetaight)$ $\Rightarrow \pi \cos 	heta=\frac{\pi}{2}-\pi \sin 	heta$ $\Rightarrow \cos 	heta+\sin 	heta=\frac{1}{2}$ Dividing both sides by $\sqrt{2}$: $\Rightarrow \frac{1}{\sqrt{2}} \cos 	heta+\frac{1}{\sqrt{2}} \sin 	heta=\frac{1}{2 \sqrt{2}}$ $\Rightarrow \cos 	heta \cos \frac{\pi}{4}+\sin 	heta \sin \frac{\pi}{4}=\frac{1}{2 \sqrt{2}}$ $\Rightarrow \cos \left(	heta-\frac{\pi}{4}ight)=\frac{1}{2 \sqrt{2}}$

If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$,then a value of $\cos \left(\theta-\frac{\pi}{4}\right)$ among the following is

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