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Question: If \(A + B = \frac{\pi}{4},\) then \((1 + \tan A)(1 + \tan B) =\)...

If A+B=π4,A + B = \frac{\pi}{4}, then (1+tan⁡A)(1+tan⁡B)=(1 + \tan A)(1 + \tan B) =

A

1

B

2

C

∞\infty

D

– 2

Answer

2

Explanation

Solution

Given that A+B=π4⇒tan⁡(A+B)=tan⁡π4A + B = \frac{\pi}{4} \Rightarrow \tan(A + B) = \tan\frac{\pi}{4}

⇒tan⁡A+tan⁡B1−tan⁡Atan⁡B=1\Rightarrow \frac{\tan A + \tan B}{1 - \tan A\tan B} = 1

⇒tan⁡A+tan⁡B+tan⁡Atan⁡B=1\Rightarrow \tan A + \tan B + \tan A\tan B = 1

⇒(1+tan⁡A)(1+tan⁡B)=2\Rightarrow (1 + \tan A)(1 + \tan B) = 2.