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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`

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The correct Answer is:
`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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