A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) None of these
Correct Answer: A
Solution :
\[\cos A\sin \left( A-\frac{\pi }{6} \right)=\frac{1}{2}\,\left[ \sin \left( 2A-\frac{\pi }{6} \right)-\sin \frac{\pi }{6} \right]\] But \[\sin \left( 2A-\frac{\pi }{6} \right)-\frac{1}{2}\] attain maximum value at \[2A-\frac{\pi }{6}=\frac{\pi }{2}\Rightarrow A=\frac{\pi }{3}\].
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