Find the range of `y = (cot^(-1) x) (cot^(-1) (-x))`

1.	Find the range of `y = (cot^(-1) x) (cot^(-1) (-x))`
Answer» `y = (cot^(-1) x) (cot^(-1) (-x))` `= cot^(-1) (x) (pi - cot^(-1) (x))` Now, `cot^(-1) (x) and (pi - cot^(-1) (x)) gt 0` Using A.M. `ge` G.M., we get `(cot^(-1) x + (pi - cot^(-1) x))/(2) ge sqrt((cot^(-1) x) (pi - cot^(-1) x))` `rArr 0 lt cot^(-1) (x) (pi - cot^(-1) (x))` `le ((cot^(-1) x + (pi - cot^(-1) x))/(2))^(2) = (pi^(2))/(4)` `rArr 0 lt y le (pi^(2))/(4)`

Discussion

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