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

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(A) Given $	an (\pi \cos 	heta ) = \cot (\pi \sin 	heta )$.Using the identity $\cot(x) = 	an\left(\frac{\pi}{2} - xight)$,we get:$	an (\pi \cos

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

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(A) Given $	an (\pi \cos 	heta ) = \cot (\pi \sin 	heta )$.Using the identity $\cot(x) = 	an\left(\frac{\pi}{2} - xight)$,we get:$	an (\pi \cos 	heta ) = 	an \left( \frac{\pi}{2} - \pi \sin 	heta ight)$.This implies $\pi \cos 	heta = \frac{\pi}{2} - \pi \sin 	heta + n\pi$ for some integer $n$.Taking $n=0$,we have $\cos 	heta + \sin 	heta = \frac{1}{2}$.Multiply both sides by $\frac{1}{\sqrt{2}}$:$\frac{1}{\sqrt{2}} \cos 	heta + \frac{1}{\sqrt{2}} \sin 	heta = \frac{1}{2\sqrt{2}}$.Using the formula $\cos(A-B) = \cos A \cos B + \sin A \sin B$,where $A = 	heta$ and $B = \frac{\pi}{4}$:$\cos \left( 	heta - \frac{\pi}{4} ight) = \frac{1}{2\sqrt{2}}$.

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

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