If tan θ + sec θ = x; what is the value of tanθ.secθ ?

tan θ + sec θ = x

⇒ tan θ - sec θ = \(\frac{1}{x}\)

4tanθ.secθ = (tanθ + secθ)² - (tanθ - secθ)²

⇒ 4tanθ.secθ = x² - \(\frac{1}{x^2}\)

⇒ tanθ.secθ = \(\frac{1}{4}\)(x² -  \(\frac{1}{x^2}\))