If $ an heta=2$ and $ heta$ lies in the third quadrant, then the value of $\sec heta$ is

Question

If $	an 	heta=2$ and $	heta$ lies in the third quadrant, then the value of $\sec 	heta$ is

Aicharya · Accepted Answer

$\sec ^{2} 	heta=1+(2)^{2}=5$ $	herefore \sec 	heta=-\sqrt{5}$ $\quad\quad\left[\because 	hetaight.$ lies in $3^{	ext {nd }}$ quadrant. $]$

If $\tan \theta=2$ and $\theta$ lies in the third quadrant, then the value of $\sec \theta$ is