Question

If cosecθ = 3x and cotθ = 3/x, then what is the value of x² - 1/x²?
1. 3
2. 1/3
3. 9
4. 1/9

Answer 1

Correct Answer - Option 4 : 1/9

Given:

cosecθ = 3x 

cotθ = 3/x

Formula used:

cosec²θ - cot²θ = 1

Calculation:

cosecθ = 3x 

⇒ cosec²θ = 9x²               [Squaring both sides]       .......(1)

cotθ = 3/x

⇒ cot²θ = 9/x²                  [Squaring both sides]      ..........(2)

Subtract (2) in (1)

cosec2θ - cot2θ = 9x2 - 9/x2 

⇒ 1 = 9(x2 - 1/x²)

⇒ (x2 - 1/x2) = 1/9

∴ The value of x2 - 1/x² is 1/9.