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If α + β = π , then the value of (1 + tanα)(1 + tanβ) is 4
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- 1
- 2
- –2
- 5
- 1
Correct Option: B
| Here, α + β = | ||
| 4 |
(1 + tanα)(1 + tanβ)
= 1 + tanβ + tanα + tanα tanβ
= 1 + tanα + tanβ + tanα tanβ
Also, we know that,
| tan (α + β) = | ||
| 1 - tanαtanβ |
| tan | = | ||
| 4 | 1 - tanαtanβ |
⇒ 1 - tanαtanβ = tanα + tanβ
⇒ (1 + tanα)(1 + tanβ)
= 1 + 1 – tanα tanβ + tanα tanβ = 2
