Question

If 2sin2 theta =root3 ,where 2 theta is acute ,then find the value of theta ?

Answer 1

Answer:

The value of theta in the given expression $2 \sin 2 \theta = \sqrt { 3 }$ is 30°  

To find:

The value of theta in the expression $2 \sin 2 \theta = \sqrt { 3 }$

Solution:

Given,

$2 \sin 2 \theta = \sqrt { 3 }$

Acute angle means the angle which is less than 90° but it must be greater than 0° i.e., the angle between 0° and 90°

$\begin{array} { c } { \sin 2 \theta = \frac { \sqrt { 3 } } { 2 } } \\\\ { \sin 2 \theta = \sin 60 ^ { \circ } } \end{array}$

Here, 2θ is acute. Thus,

$\begin{array} { c } { 2 \theta = 60 ^ { \circ } } \\\\ { \theta = \frac { 60 ^ { \circ } } { 2 } = 30 ^ { \circ } } \end{array}$

Therefore, the value of theta is,

$\theta =30^{\circ}$

Answer 2

Answer:

$Value \: of \: \theta =30\degree$

Explanation:

Given $2sin2\theta=\sqrt{3}$,

where $2\theta$ is acute.

$\implies sin2\theta=\frac{\sqrt{3}}{2}$

$\implies sin2\theta=sin60$

$\implies 2\theta = 60$

$\implies \theta = \frac{60}{2}$

$\implies \theta = 30$

Therefore,

$\theta = 30\degree$

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