Question

If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\] 

Answer 1

Given: 

`cosecθ=2x, cot θ2/x` 

We know that, 

`cosec^2 θ-cot^2 θ=1`

⇒` (2x)^2-(2/x)^2=1` 

⇒` 4x^2-4/x^2=1` 

⇒ `4(x^2-1/x^2)=1` 

⇒`2xx2xx(x^2-1/x^2)=1` 

⇒ `2(x^2-1/x^2)=1/2`