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

Given:

\( \sqrt{3} \sin x=\cos x \)

To do:

We have to find the value of \( x \).

Solution:  

\( \sqrt{3} \sin x=\cos x \)

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

We know that,

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

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

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

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

Comparing on both sides, we get,

$x=30^{\circ}$

Hence, the value of $x$ is $30^{\circ}$.

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Updated on: 10-Oct-2022

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