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

Question

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

Aicharya · Accepted Answer

Given, $	an (\pi \cos 	heta)=\cot (\pi \sin 	heta)$ $ \begin{aligned} & \Rightarrow \quad 	an (\pi \cos 	heta)=	an \left\{\frac{\pi}{2}-\pi \sin 	hetaight\} \ & \Rightarrow \quad \pi \cos 	heta=\frac{\pi}{2}-\pi \sin 	heta \ & \Rightarrow \quad \sin 	heta+\cos 	heta=\frac{1}{2} \ & \Rightarrow \quad \frac{1}{\sqrt{2}} \sin 	heta+\frac{1}{\sqrt{2}} \cos 	heta=\frac{1}{2 \sqrt{2}} \ & \Rightarrow \quad \cos 	heta \cdot \cos \frac{\pi}{4}+\sin 	heta \cdot \sin \frac{\pi}{4}=\frac{1}{2 \sqrt{2}} \ & \Rightarrow \quad \cos \left(	heta-\frac{\pi}{4}ight)=\frac{1}{2 \sqrt{2}} \end{aligned} $

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

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