Correct Answer - Option 3 : -(13/4)
Given :
(secθ - cosecθ)/secθ = 2.5/3
Formula used :
secθ = hypotenuse/base
tanθ = perpendicular/base
tanθ = sinθ/cosθ
Calculations :
(secθ - cosecθ)/secθ = 2.5/3
(secθ - cosecθ)/secθ = 5/6
⇒ 6secθ - 6cosecθ = 5secθ
⇒ secθ = 6cosecθ
⇒ sinθ = 6cosθ
⇒ tanθ = 6
(2sinθ + cosθ)/(2cosθ - sinθ)
⇒ cosθ(2sinθ/cosθ + 1)/cosθ(2 – sinθ/cosθ)
⇒ (2tanθ + 1)/(2 – tanθ)
⇒ (2 × 6 + 1)/(2 – 6)
⇒ 13/-4 = -13/4
∴ Option 3 is the correct choice.
