Question

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

Answer 1

TRIGONOMETRY :  

Trigonometry is derived from Greek words ‘tri’ , ‘gon’ and ‘metron’.  

Trigonometry is the study of the relationship between the sides and angles of a triangle.

SOLUTION:

Given :  

2 sin x/ 2 = 1

sin x/ 2 = 1/2

sin x/ 2 = sin 30°

[sin 30° = ½]

x/2 = 30°

x = 30° × 2 = 60°

x = 60°  

Hence, the value of x  is 60°.

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Answer 2

$\underline{\bold{Solution:-}}$

$2sin\frac{x}{2} =1 \\ \\ \bold{On \: dividing \: both \: sides \: by \: 2 }\\ \\ sin\frac{x}{2} = \frac{1}{2} \\ \\ {sin}^{ - 1}sin\frac{x}{2} = {sin}^{ - 1} \frac{1}{2} \\ \\ \frac{x}{2} ={sin}^{ - 1} \frac{1}{2} \\ \\ \bold{ We \: know \: that \: \:} \\ \\\bold{ \frac{1}{2} = sin \frac{\pi}{6}} \\ \bold{where \: \pi \: belongs \: to \:[ \frac{ - \pi}{2} ,\frac{\pi}{2}]} \\ \\ \frac{x}{2} ={sin}^{ - 1} \sin( \frac{\pi}{6} ) \\ \\ \frac{x}{2} = \frac{\pi}{6} \\ \\ x = 2 \times \frac{\pi}{6} \\ \\ \boxed{x = \frac{\pi}{3} }$

So, the value of x is π/3.