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