If cosec A - cot A = , then the value of tan A is :

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

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Given:

cosec A - cot A = 

Concept used:

1. cosec2 A - cot2 A = 1

2. cot A = 1 ÷ tan A

Calculation:

cosec A - cot A =       ....(1)

​According to the concept,

cosec2 A - cot2 A = 1

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

⇒ (cosec A + cot A) ×  = 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 .

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