InterviewSolution
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InterviewSolution
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If `|cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3)`, thenA. `x in [-(1)/(3), (1)/(sqrt3)]`B. `x in (-(1)/(sqrt3), (1)/(sqrt3))`C. `x in (0, (1)/(sqrt3))`D. none of these |
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Answer» Correct Answer - B We have `|cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3)` `rArr -(pi)/(3) lt cos^(-1) ((1 -x^(2))/(1 + x^(2))) lt (pi)/(3)` `rArr 0 le cos^(-1).(1 -x^(2))/(1 + x^(2)) lt (pi)/(3)` `rArr (1)/(2) lt (1 - x^(2))/(1 + x^(2)) le 1` `rArr 1 + x^(2) lt 2 (1 -x^(2)) le 2 (1 + x^(2))` `rArr 0 le x^(2) lt (1)/(3)` `rArr -(1)/(sqrt3) lt x lt (1)/(sqrt3)` |
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