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Find the maximum value of `(sec^(-1) x) (cosec^(-1) x), x ge 1` |
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Answer» Correct Answer - `(pi^(2))/(16)` For `x ge 1, cosec^(-1) x gt 0` Using A.M. `ge` G.M., we have `(sec^(-1) x + cosec^(-1) x)/(2) ge sqrt(sec^(-1) x cosec^(-1) x)` `rArr ((pi//2))/(2) ge sqrt(sec^(-1) x cosec^(-1) x)` `rArr (pi)/(2) ge sqrt(sec^(-1) x cosec^(-1) x)` `:. sec^(-1) x cosec^(-1) x le (pi^(2))/(16)` Thus maximum value of `sec^(-1) x cosec^(-1) x " is " (pi^(2))/(16)` |
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