If 4sin θ = 3cos θ, then what is the value of cosecθ ?

4sin θ =  3cos θ

⇒ \(\frac{sin θ}{cos θ}\) = \(\frac{3}{4}\)

⇒ tan θ = \(\frac{3 (P)}{4 (B)}\)

using Pythagoras theorem , 

Hypotenuse = 5

cosecθ = \(\frac{H}{P}\)= \(\frac{5}{3}\)