InterviewSolution
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InterviewSolution
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If `sin^(-1) (x^(2) + 2x + 2) + tan^(-1) (x^(2) - 3x - k^(2)) gt (pi)/(2)`, then find the value of k |
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Answer» `sin^(-1) (x^(2) + 2x + 2) + tan^(-1) (x^(2) - 3x - k^(2)) gt (pi)/(2)` `rArr sin^(-1) ((x + 1)^(2) + 1) + tan^(-1) (x^(2) - 3x - k^(2) gt (pi)/(2)` Now, `sin^(-1) ((x + 1)^(2) + 1)` is defined if `(x + 1)^(2) = 0 " or " x = -1` Putting `x = -1`, we get `(pi)/(2) + tan^(-1) (4 - k^(2)) gt (pi)/(2)` `rArr tan^(-1) (4 - k^(2)) gt 0` `rArr 4 - k^(2) gt 0` `rArr -2 lt k lt 2` |
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