SSC CGL 2022 PYQ — Question 51

The correct answer is Option 1. i.e. 8/15.

Given:

cosecA - cotA = ¼    ....(i)

Concept Used:

cosec²A - cot²A = 1   ....(ii) 

cotA = 1/tanA

Explanation:

From equation (i), we get

cosec²A - cot²A = 1

⇒ (cosecA + cotA)(cosecA - cotA) = 1

⇒ (cosecA + cotA) × ¼ = 1

⇒ cosecA + cotA = 4   ....(iii)

Now, subtracting equation (1) and equation (iii), we get

2cotA = 15/4

⇒ cotA = 15/8

⇒ tanA = 8/15

Hence the required value of tanA is 8/15.