If cosec B = 3/2, then what is the value of cot B sin B ?

$\frac{\sqrt{5}}{3}$ $\frac{4}{3\sqrt{3}}$ $\frac{3\sqrt{2}}{2}$ $\frac{2\sqrt{5}}{3}$

$\frac{\sqrt{5}}{3}$

We are given that :- cosecB = \(\frac{3}{2}\) { we know, cosecB = \(\frac{H}{P}\) } By using pythagoras theorem, P² + B² = H² 2² + B² = 3² B² = 9 - 4 = 5 B = \(\sqrt {5 }\) Now, cotB . sinB = \(\frac{B}{P}\) × \(\frac{P}{H}\) = \(\frac{ √5 }{2}\) × \(\frac{2}{3}\) = \(\frac{ √5 }{3}\)