Answer:
A) [tex]\displaystyle \frac{2\sqrt{5}}{5}[/tex]
Step-by-step explanation:
Since [tex]\csc\beta=\frac{1}{\sin\beta}[/tex], [tex]\sec\beta=\frac{1}{\cos\beta}[/tex], and [tex]\cot\beta=\frac{\cos\beta}{\sin\beta}[/tex], then [tex]\cot\beta=\frac{\csc\beta}{\sec\beta}[/tex]
This means that [tex]\displaystyle \cot\beta=\frac{-\frac{3\sqrt{5}}{5}}{-\frac{3}{2}}=\frac{-3\sqrt{5}}{5}*-\frac{2}{3}=\frac{2\sqrt{5}}{5}[/tex]
