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If y = (1 + tan A) (1 - tan B), where A ...

If y = (1 + tan A) (1 - tan B), where `A -B=pi/4` then `(y+ 1)^(y + 1)` is equal to

A

9

B

4

C

27

D

81

Text Solution

Verified by Experts

The correct Answer is:
C
`A-B=(pi)/(4)` or `tan (A-B)=tan""(pi)/(4)`
or `(tan A-tan B)/(1+tan A tan B)=1`
or `tan A-tan B-tan A tan B=1`
or `tan A-tan B -tan A tan B+1=2`
or `(1+tan A)(1-tan B)=2rARr y=2`
Hence, `(y+1)^(y+1)=(2+1)^(2+1)=(3)^(3)=27`.
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