Question

If cot θ = 4/3 and θ is an acute angle, then find the value of cosec θ.

1. 4/5
2. 5/3
3. 2
4. 1/2
5. 1/3

Answer 1

Correct Answer - Option 2 : 5/3

Given:

cot θ = 4/3

Formula used:

cosec² θ – cot² θ = 1

Calculation:

cot θ = 4/3

⇒ cosec² θ – cot² θ = 1

⇒ cosec² θ = 1 + cot² θ

⇒ cosec² θ = 1 + (4/3)²

⇒ cosec² θ = 1 + (16/9)

⇒ cosec² θ = (25/9)

⇒ cosec θ = √(25/9)

⇒ cosec θ = 5/3

∴ The value of cosecθ is 5/3.