InterviewSolution
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InterviewSolution
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If `(sin^(-1) x)^(2) - (cos^(-1) x)^(2) = a pi^(2)` then find the range of aA. `[-(3)/(4), (1)/(4)]`B. `[-(3)/(4), (3)/(4)]`C. `[-1, 1]`D. `[-1, (3)/(4)]` |
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Answer» Correct Answer - A `a pi^(2) = (sin^(-1) x)^(2) - (cos^(-1) x)^(2)` `rArr a pi^(2) = (sin^(-1) x - cos^(-1) x) (sin^(-1) x + cos^(-1) x)` `rArr a pi^(2) = (sin^(-1) x - cos^(-1) x) (pi//2)` `rArr 2 a pi = (sin^(-1) x cos^(-1) x)` `rArr 2a pi = (2 sin^(-1) x - pi//2)` Now, `-pi le 2 sin^(-1) x le pi` `rArr -3pi//2 le 2 sin^(-1) x - pi//2 le pi//2` `:. -3 pi//2 le 2a pi le pi//2` or `-3//4 le a le 1//4` |
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