InterviewSolution
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InterviewSolution
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The solution set of the inequality `tan^(-1)x+sin^(-1)x ge (pi)/(2)` isA. `[-1,1]`B. `[sqrt((sqrt(5)-1)/(4)),1]`C. `[sqrt((sqrt(5)-1)/(2)),1]`D. `[(sqrt(5)-1)/(2),1]` |
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Answer» Correct Answer - C `tan^(-1)x + sin^(-1)x ge (pi)/(2), x in [-1,1]` `rArr tan^(-1)x ge (pi)/(2) -sin^(-1)x` `rArr tan^(-1)x ge cos^(-1)x` `rArr x ge "tan"^(-1)(sqrt(1-x^(2)))/(x)` `rArr x ge (sqrt(1-x^(2)))/(x)` `x^(4)ge 1-x^(2)` `rArr x^(4)+x^(2)-1ge 0` `rArr x in [sqrt((sqrt(5)-1)/(2)),1]` |
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