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Let `f(x)=sin^(-1)((2x)/(1+x^(2)))` and `g(x)=cos^(-1)((x^(2)-1)/(x^(2)+1))`. Then tha value of f(10)-g(100) is equal toA. `pi-2(tan^(-1)(10)+tan^(-1)(100))`B. 0C. `2(tan^(-1)(100)-tan^(-1)(10))`D. `2(tan^(-1)(10)-tan^(-1)(100))` |
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Answer» Correct Answer - C `f(x)=sin^(-1)((2x)/(1+x^(2)))=pi-2 tan^(-1)x`, for `x ge 1` and `g(x)=cos^(-1)((x^(2)-1)/(x^(2)+1))` `=pi-cos^(-1)((1-x^(2))/(1+x^(2)))` `=pi-cos^(-1)((1-x^())/(1+x^(2)))` `=pi -2 tan^(-1)x`, for `x ge 0` Now f(10)-g(100) `=(pi-2tan^(-1)(10))-(pi-2tan^(-1)(100))` `=2(tan^(-1)(100)-tan^(-1)(10))` |
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