Trigonometric-Equations Question 393

Question: If $ \cos A\sin ( A-\frac{\pi }{6} ) $ is maximum, then the value of A is equal to

Options:

A) $ \frac{\pi }{3} $

B) $ \frac{\pi }{4} $

C) $ \frac{\pi }{2} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \cos A\sin ( A-\frac{\pi }{6} )=\frac{1}{2},[ \sin ( 2A-\frac{\pi }{6} )-\sin \frac{\pi }{6} ] $ But $ \sin ( 2A-\frac{\pi }{6} )-\frac{1}{2} $ attain maximum value at $ 2A-\frac{\pi }{6}=\frac{\pi }{2}\Rightarrow A=\frac{\pi }{3} $ .

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