-
If α + β = π , then the value of (1 + tanα)(1 + tanβ) is 4
-
- 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