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Evaluate lim(xto1) (1-x)"tan"(pix)/(2)....

Evaluate `lim_(xto1) (1-x)"tan"(pix)/(2).`

Text Solution

Verified by Experts

The correct Answer is:
`2//pi`
`underset(xto1)lim(1-x)"tan"(pix)/(2)=underset(xto1)lim((1-x))/(tan((pi)/(2)-(pix)/(2)))`
`=(2)/(pi)underset(xto1)lim((2)/(pi)(1-x))/(tan((pi)/(2)(1-x)))`
`=(2)/(pi)`
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