If 3 sin θ-4 cos θ=0, then value of tan θ.cosec θ is:

3sinθ−4cosθ=0

3sinθ = 4cosθ

Tanθ = 4/3

Cotθ = 3/4

(Cotθ)^2 = (3/4)^2

1+ (Cotθ)^2 = 1+ (3/4)^2

(Cosecθ)^2 = 1+ 9/16 = 25/16

Cosecθ = 5/4

Tanθ.Cosecθ = 4/3 * 5/4 = 5/3

The correct answer is Option (3) → $\frac{5}{3}$