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Solve : `tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1)/(x+2)=pi/4` |
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Answer» Correct Answer - `x = sqrt((5)/(2))` `tan^(-1).(x -1)/(x + 2) + tan^(-1).(x + 1)/(x + 2) = (pi)/(4)` `rArr tan^(-1) [((x -1)/(x + 2) + (x + 1 )/(x + 2))/(1 - ((x -1)/(x + 2)) ((x +1)/(x + 2)))] = (pi)/(4)` `rArr [(2x (x + 2))/(x^(2) + 4 + 4x -x^(2) + 1)] = tan.(pi)/(4)` `rArr (2x (x + 2))/(4x + 5) = 1` `rarr 2x^(2) + 4x = 4x + 5` `:. x = +- sqrt((5)/(2))` But for `x = -sqrt5//2`, L.H.S. is negative Hence, `x = sqrt(5//2)` |
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