Question

The value of x for maximum value of $(\sqrt{3}\sin x + \cos x)$ is

• A. 30^o
• B. 45^o
• C. 60^o
• D. 90^o

Answer 1

Answer: (C)

60^o

Answer 2

The greatest value of $\sqrt{3}\sin x + \cos x$ is $\sqrt{3 + 1} = 2$ and

obviously it will be at $x = 60{^\circ}$.

Aliter : $2\left( \frac{\sqrt{3}}{2}\sin x + \frac{1}{2}\cos x \right) = 2\sin\left( x + \frac{\pi}{6} \right)$

As $\sin x$ is maximum at $x = \frac{\pi}{2},$ so $x + \frac{\pi}{6} = \frac{\pi}{2}$ or $x = \frac{\pi}{3}$.