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If alpha+beta=pi/4 then (1+tan alpha)(1+...

If `alpha+beta=pi/4` then `(1+tan alpha)(1+tan beta)=`

A

1

B

2

C

-2

D

Not defined

Text Solution

Verified by Experts

The correct Answer is:
B
Given that, `alpha+beta=(pi)/(4)`
Now, `" "(1+tanalpha)(1+tanbeta)=1+tanalpha+tanbeta+tanalphatanbeta" "...(i)`
We know that, `" "tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalpha*tanbeta)`
` rArr" "1=(tanalpha+tanbeta)/(1-tanalpha*tanbeta)`
`rArr" "tanalpha+tanbeta=1-tanalphatanbeta`
From Eq. (i),
`" "(1+tanalpha)(1+tanbeta)=1+1-tanalpha*tanbeta+tanalpha*tanbeta`
= 2
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