SSC CHSL 2023 PYQ — Question 58

The correct answer is option 4 i.e. ${a^2+1}\over 2a$.

Given, tanθ + secθ = a    ...(i)

tan²θ - sec²θ = 1

⇒ (tanθ - secθ)(tanθ + secθ) = 1

⇒ tanθ - secθ = 1/a    ...(ii)

Subtracting equation (ii) from equation (i),

⇒ 2secθ = a - 1/a

⇒ secθ = ${a^2+1}\over 2a$