If sec β + tan β = 2, then what is the value of cot β?

Question

Question

This question was previously asked in

SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 17 March, 2023 Shift 2)

Answer 1

Concept:

Some useful formulas are,

sec2 θ - tan2 θ = 1

tan θ =

Calculation:

We know that,

sec2 θ - tan2 θ = 1; which can be written as,

(sec θ + tan θ)(sec θ - tan θ) = 1

Since,sec β + tan β = 2 ....(1)

We can write the above equation as,

⇒ (sec β - tan β ) = ...(2)

By solving eq(1) and eq(2) we get,

2 tan β = 2 - =

⇒ tan β =

⇒ cot β =

∴ Option 3 is the correct answer.

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