If cosec A - cot A = \(\frac{1}{4}\), then the value of tan A is :

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Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2)

Answer 1

Given:

cosec A - cot A = \(\frac{1}{4}\)

Concept used:

1. cosec2 A - cot2 A = 1

2. cot A = 1 ÷ tan A

Calculation:

cosec A - cot A = \(\frac{1}{4}\) ....(1)

According to the concept,

cosec² A - cot² A = 1

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

⇒ (cosec A + cot A) × \(\frac{1}{4}\) = 1

⇒ (cosec A + cot A) = 4 ....(2)

Now, (2) - (1),

2cot A = 4 - 1/4

⇒ cot A = 15/8

⇒ tan A = 8/15

∴ The required value of tan A is \(\frac{8}{15}\).