SSC CHSL 2022 PYQ — Question 70

The correct answer is option 3 i.e.  $\frac{1}{2}(5+\frac{1}{5})$

Given:

cosec θ + cot θ = 5    ..(i)

Formula Used:

cosec²θ - cot²θ = 1

Explanation:

cosec²θ - cot²θ = 1

⇒ (cosecθ + cotθ)(cosecθ - cotθ) = 1

According to the given question,

⇒ 5(cosecθ - cotθ) = 1

⇒ (cosecθ - cotθ) = $1 \over 5$   ....(ii)

Now, adding equation (i) and equation(ii), we get

2 cosec θ = 5 + $1 \over 5$

⇒ cosec θ = $\frac{1}{2}(5+\frac{1}{5})$

Hence the required answer is $\frac{1}{2}(5+\frac{1}{5})$.