If `alpha and beta (alpha gt beta)` are the roots of `x^(2) + kx - 1 =0`, then find the value of `tan^(-1) alpha - tan^(-1) beta`

If `alpha and beta (alpha gt beta)` are the roots of `x^(2) + kx - 1 =

1.	If `alpha and beta (alpha gt beta)` are the roots of `x^(2) + kx - 1 =0`, then find the value of `tan^(-1) alpha - tan^(-1) beta`
Answer» Correct Answer - `pi` We have `alpha beta = -1 and alpha gt beta` `rArr tan^(-1) alpha gt tan^(-1) beta` `:. Tan^(-1) alpha - tan^(-1) beta = tan^(-1).(alpha - beta)/(1 + alpha beta)` `= tan^(-1) oo = (pi)/(2)`

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