Answer
III quadrant.
Work Step by Step
We know that $\tan\theta=\frac{y}{x}$ and $\sec \theta=\frac{1}{\cos \theta}=\dfrac{R}{x}.$ Where $R$ is always $R>0$.
If $\tan\theta > 0$ then ($y>0$ and $x>0$) or ($y<0$ and $x<0$). It's true for I quadrant and III quadrant.
if $\sec \theta <0$ then $x<0.$ It's true for II and III quadrants.
Both conditions are true only for III quadrant.
