यदि `tan^(-1)""(x-1)/(x-2)+tan^(-1)""(x+1)/(x+2)=(pi)/(4)`, तो `x` का मान ज्ञात कीजिए।

Explanation

`tan^(-1)""(x-1)/(x-2)+tan^(-1)""(x+1)/(x+2)=(pi)/(4)`
`impliestan^(-1)""((x-1)/(x-2)+(x+1)/(x+2))/(1-(x-1)/(x-2).(x+1)/(x+2))=tan^(-1)1`
`implies((x-1)+(x+2)+(x+1)(x-2))/((x-2)(x+2)-(x-1)(x+1))=1`
`implies(x^(2)+x-2+x^(2)-x-2)/((x^(2)-4)-(x^(2)-1))=1`
`implies(2x^(2)-4)/(-3)=1implies2x^(2)-4=-3`
`implies2x^(2)=1impliesx^(2)=(1)/(2)impliesx=+-(1)/(sqrt2)`