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" Let "f(x)=sin^(-1)((2x)/(1+x^(2)))+cos...

" Let "f(x)=sin^(-1)((2x)/(1+x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))

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sin[cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))]=

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sin{tan^(-1)[(1-x^(2))/(2x)]+cos^(-1)[(1-x^(2))/(1+x^(2))]}=