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

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

= \(\frac{B}{P}\) × \(\frac{P}{H}\)

= \(\frac{ √5 }{2}\) × \(\frac{2}{3}\)

= \(\frac{ √5 }{3}\)