Question

The maximum value of $\sin\left( x + \frac{\pi}{6} \right) + \cos\left( x + \frac{\pi}{6} \right)$ in the interval $\left( 0,\frac{\pi}{2} \right)$is attained at

• A. $x = \frac{\pi}{12}$
• B. $x = \frac{\pi}{6}$
• C. $x = \frac{\pi}{3}$
• D. $x = \frac{\pi}{2}$

Answer 1

Answer: (A)

$x = \frac{\pi}{12}$

Answer 2

$\sqrt{2}\cos\left( x + \frac{\pi}{6} - \frac{\pi}{4} \right) = \sqrt{2}\cos\left( x - \frac{\pi}{12} \right)$.

Hence maximum value will be at $x = \frac{\pi}{12}$.