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Prove the following: `tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2))` |
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Answer» We know, `tan^-1a+tan^-1b = tan^-1((a+b)/(1-ab))` `:. L.H.S. = tan^-1x+tan^-1((2x)/(1-x^2)) = tan^-1((x+((2x)/(1-x^2)))/(1-x((2x)/(1-x^2))))` `=tan^-1((x-x^3+2x)/(1-x^2-2x^2))` `=tan^-1((3x-x^3)/(1-3x^2))` `=R.H.S.` |
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