Question

If $\tan \theta =\frac{1}{\sqrt{3}}$, then find the value of $sec\theta .$

Answer 1

Finding the value of $sec\theta :$

Given, $\tan \theta =\frac{1}{\sqrt{3}}$

Using trigonometric identity,
${\sec }^2\theta -{\tan }^2\theta =1$

$\therefore {\sec }^2\theta =1+{\tan }^2\theta =1+{\left(\frac{1}{\sqrt{3}}\right)}^2=1+\frac{1}{3}=\frac{4}{3}$
$\Rightarrow \sec \theta =\frac{2}{\sqrt{3}}$

Hence, the value of $\sec \theta =\frac{2}{\sqrt{3}}$.