InterviewSolution
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InterviewSolution
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If `sin^(-1)(1-x) sin^(-1)x=(pi)/(2)` then x equalA. `-1/2`B. 1C. 0D. `1/2` |
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Answer» We have, `sin^(-1)(1-x)-2sin^(-1)x=pi/2` `sin^(-1)(1-x)=pi/2+2sin^(-1)x` `1-x=sin((pi)/(2)+sin ^(-1)x)` `1-x+cos (2sin^(-1)x)` `1-x=cos(2sin^(-1)x)` `1-x=cos[cos^(-1)(1-2x^(2))]` `1-x=1-2x^(2)` `2x^(2)-x=0` ` x(2x-1)=0` `therefore x=0or x=1/2` For `x=1/2` `sin^(-1)(1-x)-2sin^(-1)((1)/(2))-2sin^(-1)((1)/(2))=-sin^(-1)((1)/(2))=(-pi)/(6)` So, `x=1/2` is not the solution of the given equation. For `x=0` `sin^(-1)(1-x)-2sin^(-1)(1)-2sin^(-1)(0)` `=pi/2-0=pi/2` Hence, the correct anaswer from the given alternative is (c). |
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