If tan θ = $$\frac 34$$​ and θ is an acute angle, find the value of cosecθ.

Correct option is B

Given
tan θ = $$\frac 34$$​​
θ is an acute angle
Formula Used
​$$\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \\\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2\\\text{cosec } \theta = \frac{\text{Hypotenuse}}{\text{Opposite}}\\$$​​
Solution
Based on tan θ, Opposite side = 3 and Adjacent side = 4
Using Pythagoras theorem:
Hypotenuse = $$\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$​​
cosec θ = $$\frac{5}{3}$$​​
Final Answer
So the correct answer is (b)