Question

If $\sec \theta +\tan \theta =\frac{1}{5}$ then $\theta$ lies in quadrant no. _

Answer 1

$\sec \theta +\tan \theta =\frac{1}{5}\to 1$

$(\sec \theta +\tan \theta )\left(\sec {\theta }^2\tan \theta \right)=1$

$\sec \theta -\tan \theta =5\to 2$

Adding both equations $1+2$

$2\sec \theta =5+\frac{1}{5}$

$2\sec \theta =\frac{26}{5}$

$\sec \theta =\frac{13}{5}$

$\cos \theta =\frac{5}{13}$

$\therefore \theta$ lies in $4^{th}$ quadrant