Question

If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\] 

Answer 1

Given: 

`5x=sec θ, 5/x=tan θ` 

⇒ `secθ=5x, tan θ=5/x`

We know that, 

`sec^2 θ-tan^2=1` 

⇒` (5x)^2-(5/x)^2=1` 

⇒ `25x^2-25/x^2=1`  

⇒ `25(x^2-1/x^2)=1`

⇒`5xx5xx(x^2-1/x^2)=1` 

⇒` 5(x^2-1/x^2)=1/5`