If tan (α + β) = a, tan (α - β) = b, then the value of tan 2α is :

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 4)

Answer 1

Given:

tan (α + β) = a,

tan (α - β) = b

Formula used:

Tan (A + B) = (tan A + tan B)/{1 - (tanA × tanB)}

Calculation:

We can write 2α as:

⇒ 2α = (α + β) + (α - β)

Multiplying both sides with 'tan'

⇒ tan 2α = tan {(α + β) + (α - β)}

⇒ tan 2α = {tan (α + β) + tan(α - β)}/{1 - tan (α + β) × tan(α - β)}

Putting tan (α + β) = a, and tan (α - β) = b

⇒ tan 2α = (a + b)/(1 - ab)

∴ The correct answer is (a + b)/(1 - ab).

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