Question

If tan(α + β) = 4, and tan(α - β) = 3, then tan(2β) is equal to
1. 7/13
2. 1/13
3. -3/11
4. -1
5. None of these

Answer 1

Correct Answer - Option 2 : 1/13

Concept:

tan(A - B) = \(\rm \frac{tan A-tanB}{1+tanAtanB}\)

Calculation:

Here, tan(α + β) = 4, and tan(α - β) = 3

∴ tan [(α + β) - (α - β)] = \(\rm \frac{tan (\alpha+β) -tan (\alpha+β) }{1+tan (\alpha+β) tan (\alpha-β) }\)

⇒ tan (2β) = \(\frac{4-3}{1+(4)(3)}\)

= 1/13

Hence, option (2) is correct.