Question

What quadrant does sec(theta)>0 and cot(theta)<0 lie in

Answer 1

$\sec\theta=\dfrac1{\cos\theta}>0\implies\cos\theta>0$

This happens in the first and fourth quadrants.

Since cosine is positive,

$\cot\theta=\dfrac{\cos\theta}{\sin\theta}$

and this happens in the third and fourth quadrants.

This means both conditions can only occur in the fourth quadrant.