If tan θ + sec θ = 2 ; what is the value of tanθ.secθ ?

tan θ + sec θ = 2

⇒ secθ - tan θ = \(\frac{1}{2}\)

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

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

⇒ tanθ.secθ = \(\frac{1}{4}\)(4 - \(\frac{1}{4}\))  = \(\frac{15}{16}\)