\(\sec\theta=\dfrac1{\cos\theta}>0\implies\cos\theta>0\)
This happens in the first and fourth quadrants.
Since cosine is positive,
\(\cot\theta=\dfrac{\cos\theta}{\sin\theta}<0\implies\sin\theta<0\)
and this happens in the third and fourth quadrants.
This means both conditions can only occur in the fourth quadrant.
