Question

The maximum value of the function
$ f(x)=\sin (x+\pi /6)+\cos (x+\pi /6) $
in the interval $ (0,\text{ }\pi /2) $ occurs at

• A. $ \pi /12 $
• B. $ \pi /6 $
• C. $ \pi /4 $
• D. $ \pi /3 $

Answer 1

Answer: (A)

Maximum value of $ f(x)=\sqrt{2}, $
when $ x+\pi /6=\pi /4 $ i.e.,
when $ x=\frac{\pi }{12} $