InterviewSolution
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InterviewSolution
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If `-1lexle0` then `sin^(-1)x` equalsA. `pi-sin^(-1)sqrt(1-x^(2))`B. `tan^(-1)(x)/sqrt(1-x^(2))`C. `-cot^(-1)sqrt(1-x^(2))/(x)`D. none of these |
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Answer» Let `sin^(-1)x=theta` Then `x =sin theta` Now `-1 lt x lt 0 rarr-(pi)/(2)ltthetalt0` `pi-sin^(-1)sqrt(1-x^(2))` `=pi-sin^(-1)(cos theta)` `As-(pi)/(2)ltthetalt0` `therefore 0ltpi-thetalt(pi)/(2)rarr 0ltpi-sin^(-1)sqrt(1-x^(2))lt(pi)/(2)` `therefore sin^(-1)x ne pi-sin^(-1)sqrt(1-x6(2))` So option (a) is not correct we have `tan^(-1)(x)/sqrt(1-x^(2))` `=tan^(-1)(sin htheta)/(sqrt(1-sin^(2)theta)=tan^(-1)(tan theta)=theta =sin^(-1)x` Thus option (b) is correct We have `-cot^(-1)sqrt(1-x^(2))/(x)=cos^(-1)(cos theta)//(sin theta)=-cos^(-1)(cot theta)` `=cosT^(-1)(cos(-theta))` `-theta` `-sin^(-1)x` Thus option (c ) is also not correct |
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