Find the value of $ x $ in each of the following:$ 2 \sin \frac{x}{2}=1 $

Given:

\( 2 \sin \frac{x}{2}=1 \)

To do:

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

Solution:  

$2 \sin \frac{x}{2}=1$

$\Rightarrow \sin \frac{x}{2}=\frac{1}{2}$

We know that,

$\sin 30^{\circ}=\frac{1}{2}$

$\Rightarrow \sin \frac{x}{2}=\frac{1}{2}$

$\Rightarrow \sin \frac{x}{2}=\sin 30^{\circ}$

Comparing on both sides, we get,

$\frac{x}{2}=30^{\circ}$

$x=2(30^{\circ})$

$x=60^{\circ}$

Hence, the value of $x$ is $60^{\circ}$. 

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Updated on: 10-Oct-2022

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