A) \[\frac{1}{2\sqrt{2}}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\frac{1}{3\sqrt{2}}\]
D) \[\frac{1}{4\sqrt{2}}\]
Correct Answer: A
Solution :
\[\tan (\pi \cos \theta )=\tan \left( \frac{\pi }{2}-\pi \sin \theta \right)\] \[\therefore \] \[\,\sin \theta +\cos \theta =\frac{1}{2}\]\[\Rightarrow \,\cos \left( \theta -\frac{\pi }{4} \right)=\frac{1}{2\sqrt{2}}\].
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