Question

The value of $\sqrt{3}\sin x+\cos x$ is max. when $x$ is equal to

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

Answer 1

The correct option is C ${60}^o$

Given expression

$f\left(x\right)=\sqrt{\sin }x+\cos x$

For the equation to be maximum

$f^{\prime }\left(x\right)=0$

$⟹\frac{d}{dx}(\sqrt{3}\sin x+\cos x)$

$⟹\sqrt{3}\cos x-\sin x=0$

$⟹\sqrt{3}\cos x=\sin x$

$⟹\tan x=\sqrt{3}$

$⟹x={60}^{\circ }$