Question

Find the value of $\theta :$

$cosec4\theta =\frac{2}{\sqrt{3}}$

Answer 1

Solving the given expression:

In order to determine the value of $\theta$, we will simplify the given expression,

$\begin{array}{rcl}cosec4\theta & =& \frac{2}{\sqrt{3}}\\ & \Rightarrow & cosec4\theta =cosec60°\left[\because \cos ec60°=\frac{2}{\sqrt{3}}\right]\\ \Rightarrow 4\theta & =& 60°\\ \Rightarrow \theta & =& \frac{60}{4}=15°\end{array}$

Hence, the value of $\theta$ in the given expression will be $15°$.