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