If A + B = 45º, then the value of 2(1 + tanA)(1 + tanB) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 4
| Understanding | Application |
| Tricks |
Given A + B = 45º We know tan(A + B) = (tanA + tanB)/(1 - tanA.tanB) |
| Now |
⇒ tan45 = (tanA + tanB)/(1 - tanA.tanB) ⇒ 1 = (tanA + tanB)/(1 - tanA.tanB) ⇒ 1 - tanA.tanB = tanA + tanB ⇒ 1 = tanA + tanB + tanA.tanB ⇒ 1 + 1 = 1 + tanA + tanB(1 + tanA) (adding 1 in both sides) ⇒ 2 = (1 + tanA) (1 + tanB) |
| Hence |
⇒ 2(1 + tanA) (1 + tanB) = 2 × 2 = 4 |