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Solve : tan − 1 ( x − 1 / x − 2 ) + ta...

Solve : tan − 1 ( x − 1 / x − 2 ) + tan − 1 ( x + 1 / x + 2 ) = π / 4 Then find the value of x.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(pi)`
`'f(0)=underset(xrarr0)lim(f(x)-f(0))/(x-0)`
`=underset(xrarr0)lim((2^(x)+2^(-x))(sin x)/(x)sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(2))`
`=(2xx1sqrt(tan^(-1)1))/((0+0+1)^(3))`
`=sqrt(pi)`
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