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Solution set of inequation`(cos^(-1)x)^(2)-(sin^(-1)x)^(2)gt0` isA. `[0,(1)/sqrt(2))`B. `[-1,(1)/sqrt(2))`C. `[-1,sqrt(2))`D. None of these |
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Answer» Correct Answer - B Given, `(cos^(-1)x)^(2)-(sin^(-1)x)^(2)gt0` `ltimplies(cos^(-1)x+sin^(-1)x)(cos^(-1)x-sin^(-1)x)gt0` `ltimplies(pi)/(2)(cos^(-1)x sin^(-1) x)gt 0` `ltimplies cos^(-1)x-sin^(-1)x gt 0` `ltimplies (pi)/(2)-2sin^(-1)xgt0 ltimplies -1le x lt (1)/sqrt(2)` `[ because "for" cos^(-1) x "and" sin^(-1) x "to be defined" -1 le x le 1 ]` |
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