Solve:3tan−1x=tan−1(1−3x23x−x3 )

tan−1A+tan−1B=tan−1(1−ABA+B)⇒3tan−1x=tan−1x+tan−1x+tan−1x=tan−1(1−x22x)+tan−1x=tan−1⎝⎛1−1−x2x−2x1−x22x+x⎠⎞=tan−1(1−3x23x−x3)=R.H.S.

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Solve: 3 ^{ -1 }{ x } = ^{ -1 }{ ( { 3x-{ x }^{ 3 } }{ 1-3{ x

Question

Solve:
$3 tan^{- 1} x = tan^{- 1} (\frac{3 x - x ^{3}}{1 - 3 x ^{2}})$

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Amelia Discussed

Solve:

3 tan^{- 1} x = tan^{- 1} (\frac{3 x - x ^{3}}{1 - 3 x ^{2}})

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tan^{- 1} A + tan^{- 1} B = tan^{- 1} (\frac{A + B}{1 - A B})

\Rightarrow 3 tan^{- 1} x = tan^{- 1} x + tan^{- 1} x + tan^{- 1} x = tan^{- 1} (\frac{2 x}{1 - x ^{2}}) + tan^{- 1} x

= tan^{- 1} ⎝ ⎛ \frac{\frac{2 x}{1 - x ^{2}} + x}{1 - \frac{x - 2 x}{1 - x ^{2}}} ⎠ ⎞ = tan^{- 1} (\frac{3 x - x ^{3}}{1 - 3 x ^{2}}) =

R.H.S.

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