If 5x = secθ and 5/x = tanθ, find the value of 5(x^2 - 1/x^2).

Question

If 5x = secθ and \(\frac{5}{x}\) = tanθ, find the value of 5\(\Big(x^2-\frac{1}{x^2}\Big)\)

Answer 1

Given: 5x = sec θ

⇒ x = \(\frac{secθ}{5}\)

⇒ x² = \(\frac{sec^2θ}{25}\).....(i)

And \(\frac{5}{x}\)=tanθ

⇒ x = \(\frac{5}{tanθ}\)

⇒ x² = \(\frac{25}{tan^2θ}\)

⇒ \(\frac{1}{x^2}\) = \(\frac{tan^2θ}{25}\).....(ii)

To find: 5\(\Big(x^2-\frac{1}{x^2}\Big)\)