InterviewSolution
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InterviewSolution
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If `0lexle1` then `sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^(2)))}` is equal toA. 1B. `-1`C. 0D. none of these |
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Answer» We know that `tan^(-1)((2x)/(1-x^(2))=2 tan^(-1)x if -1 ltx le1` and `therefore sin{ tan^(-1)(1-x^(2))/(2x)+cos^(-1)(1-x^(2))/(1+x^(2))}` `=sin{cot^(-1)(2x)/(1-x^(2))+cos^(-1)(1-x^(2))/(1+x^(2))` `=sin{(pi)/(2)-2tan^(-1) x+2 tan^(-1)x} if 0 le x lt1` `=sin(pi)/(2)=1` |
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