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If alphaand beta are positive angles s...

If `alphaand beta` are positive angles such that `alpha=beta=(pi)/(4)`,then what is `(1-tanalpha)(1+tanbeta)` equal to ?

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Let `alpha+beta=(pi)/(4)`
`rArrtan(alpha+beta)="tan"(pi)/(4)`
`rArrtan(alpha+tanbeta)/(1-tanalphatanbeta)=1`
`rArrtanalpha+tanbeta=1-tanalphatanbeta`
By adding 1 on both sides , we get `1+tanalpha+tanbeta+tanalphatanbeta=2`
`rArr(1+tanalpha)(1+tanbeta)=2`
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