Find the value of x in each of the following :

Solution:

We have,

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

Now by cross multiplying we get,

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

$\Rightarrow \frac{\sin x}{\cos x}=\frac{1}{\sqrt{3}}$.....(1)

Now we know that

$\frac{\sin x}{\cos x}=\tan x$....(2)

Therefore from equation (1) and (2)

We get,

$\tan x=\frac{1}{\sqrt{3}}$.....(3)

Since,

$\tan 30^{\circ}=\frac{1}{\sqrt{3}}$....(4)

Therefore, by comparing equation (3) and (4) we get,

$x=30^{\circ}$

Therefore,

$x=30^{\circ}$