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The number of roots of the equation `sin^(-1)x-(1)/(sin^(-1)x)=cos^(-1)x-(1)/(cos^(-1)x)` is |
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Answer» Correct Answer - C `sin^(-1) x-(1)/(sin^(-1)x)=cos^(-1)x-(1)/(cos^(-1)x)` `rArr (sin^(-1)x-cos^(-1)x)((sin^(-1)x.cos^(-1)x+1))/(sin^(-1)x.cos^(-1)x)=0` `rArr sin^(-1)x=cos^(-1)x` or `sin^(-1)x cos^(-1)x+1=0` `rArr x=(1)/(sqrt(2))` or `sin^(-1)x((pi)/(2)-sin^(-1)x)+1=0` `rArr x=(1)/(sqrt(2))` or `sin^(-1)x=((pi)/(2)pm sqrt(((pi^(2))/(4)+4)))/(2)` `rArr x = (1)/(sqrt(2))` or `sin^(-1)x=(pi)/(4)-sqrt((1+(pi^(2))/(16)))` |
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