SSC CGL 2018 PYQ — Question 50

The correct answer is option 3 i.e. (x² – 4)/(x² + 4)

tan θ + sec θ = (x – 2)/(x + 2)

So,

secθ - tanθ = (x + 2)/(x - 2) .....(1)

secθ + tanθ = (x - 2)/(x + 2) .....(2)

Adding (1) and (2), we get:

⇒ 2 secθ = (x + 2)/(x - 2) + (x - 2)/(x + 2) = (x + 2)²+(x - 2)²/ x²-4

⇒ 2 secθ = 2(x² + 4)/(x² - 4)

⇒ secθ = (x² + 4)/(x² - 4)

⇒ cosθ = (x² - 4)/(x² + 4)