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If the function f(x) = (1-x) tan ""(pix...

If the function f(x) = (1-x) ` tan ""(pix)/2` is continuous at x =1 then f (1) =

A

`(2)/(pi)`

B

`(pi)/(2)`

C

0

D

`2pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`f(1)=lim_(x to 1) f(x) =lim_(x to 1) (1-x) tan ((pi x)/(2))`
`=lim_(x to 0) (1-(1+h)) tan ((pi)/(2) (1+h))`
`=lim_(h to 0) (-h) tan ((pi)/(2) +(pi h)/(2))`
`=lim_(h to 0) (-h) (-"cot"(pih)/(2))`
`=lim_(h to 0) ((pi)/(2)*h)/(tan((pih)/(2))*(2)/(pi)=(2)/(pi))`
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