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Prove the following: tan^(-1)x+tan^(-1)(...

Prove the following: `tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2))`

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Solving L.H.S

`tan ^{-1} x+\tan ^{-1} \frac{2 x}{1-x^{2}}`

We know that `\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}(\frac{x+y}{1-xy})` Replacing `y` by `\frac{2 x}{1-x^{2}}`

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[ If xgt0 then which of the following is true 1) tan^(-1)xgt(x)/(1+x^(2)), 2) tan^(-1)x=(x)/(1+x^(2)) 3) tan^(-1)xlt(x)/(1+x^(2)), 4) tan^(-1)x!=(x)/(1+x^(2))]