Question

Find the value of $x$ in the following
$\sqrt{3}\sin x=\cos x$

Answer 1

Given $\sqrt{3}\sin x=\cos x$

$\frac{\sin x}{\cos x}=\frac{1}{\sqrt{3}}$

we know that,

$\tan x=\frac{\sin x}{\cos x}$

$\tan x=\frac{1}{\sqrt{3}}$

Also, $\tan {30}^{\circ }=\frac{1}{\sqrt{3}}$

$\Rightarrow \tan x=\tan {30}^{\circ }$

$\therefore x={30}^{\circ }$