SSC CPO 2023 PYQ — Question 130

The correct answer is option 4 i.e. $\frac{4}{5}$

Given:

cosec A + cot A = 3            ---- (1)

Concept used:

cosec²A - cot²A = 1

Calculations:

According to the question;

⇒ (cosec A - cot A)(cosec A + cot A) = 1

⇒ (cosec A - cot A) = 1/3            ---- (2)

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

⇒ 2 cosec A = 10/3

⇒ cosec A = 5/3 or sin A = 3/5

⇒ sin A = 3/5 = Perpendicular/hypotenuse

using pythagoras theorem,

⇒ Hypotenuse² = base² + perpendicular²

⇒ 5² = base² + 3²

⇒ base = 4

We know that, cos A = base/hypotenuse

⇒ cos A = 4/5