[tex]\csc\theta=\dfrac1{\sin\theta}>0\implies\sin\theta>0[/tex]
This happens whenever the terminal point of [tex]\theta[/tex] lies in either the first or second quadrants.
Meanwhile,
[tex]\cot\theta=\dfrac1{\tan\theta}=\dfrac{\cos\theta}{\sin\theta}>0\implies\cos\theta>0[/tex]
since you already know sine is positive. Cosine is positive when the angle lies in the first or fourth quadrant.
Sine and cosine are both positive only when [tex]\theta[/tex] is the first quadrant, which means this angle's terminal point lies in the first quadrant (A).
