Question

Find the value $x$ for a given trigonometric equation $se{c}^{-1}\left[sec\right(-{30}^0\left)\right]$

Answer 1

Evaluate the value of $x$

Let, $x=se{c}^{-1}\left[sec\right(-{30}^0\left)\right]$

$\Rightarrow secx=sec(-{30}^0)$

$\Rightarrow$$secx=sec\left({30}^0\right)\left[\therefore sec\left(-\theta \right)=sec\theta \right]$

$\Rightarrow$$secx=\frac{2}{\sqrt{3}}\left[\therefore sec{30}^0=\frac{2}{\sqrt{3}}\right]$

$\Rightarrow$ $x=se{c}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

$\Rightarrow$ $x=\frac{\mathrm{\pi }}{6}$

Hence, the value of $x$ is $\frac{\mathrm{\pi }}{6}$.