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The function `f(x)=(1-sinx+cosx)/(1+sinx+cosx)` is not defined at `x=pi`.
The value of `f(pi)` so that f(x) is continuous at `x=pi` is

A

`-(1)/(2)`

B

`(1)/(2)`

C

`-1`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xto""pi)lim(1-sinx+cosx)/(1+sinx+cosx)`
Using L' hosptial' s rule
`impliesunderset(xto""pi)lim(-cosx-sinx)/(cosx-sinx)`
`implies(-cospi-sinpi)/(cospi-sinpi)`
`implies(-(-1)-0)/(-1-0)`
`implies-1`
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