SSC CHSL 2023 PYQ — Question 51

The correct answer is option 1 i.e. ${3 \sqrt3}\over 2$.

If secθ - tanθ = x then

secθ + tanθ = 1/x

So,

⇒ secθ + tanθ = $1\over \sqrt3$ ....(1)

⇒ secθ - tanθ = $\sqrt3$ .....(2)

From equation 1 and 2

⇒ 2secθ = $1\over \sqrt3$ + $\sqrt3$

⇒ 2secθ = $4\over \sqrt3$

⇒ secθ = $2\over \sqrt3$

⇒ secθ = sec 30°

⇒ θ = 30°

Now,

The value of  cot θ + cos θ

⇒ cot 30° + cos 30°

⇒ $\sqrt3$ + $\sqrt3 \over 2$ = $3\sqrt3 \over 2$