The root of the equation tan-1x-1-x-1 -tan-12x-1-2x-1 -tan-123-36 is

2x^2 1/3x=23/36⇒ x =4/3, 3/8 but x can not be negative. ...

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Properties Derived from Trigonometric Identities

The root of t...

Question

The root of the equation $t a n^{- 1} (\frac{x - 1}{x + 1}) + t a n^{- 1} (\frac{2 x - 1}{2 x + 1}) = t a n^{- 1} (\frac{23}{36})$ is

- \frac{3}{8}

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- \frac{1}{2}

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\frac{3}{4}

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\frac{4}{3}

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Solution

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{tan}^{- 1} (\frac{x - 1}{x + 1}) + {tan}^{- 1} (\frac{2 x - 1}{2 x + 1}) = {tan}^{- 1} \frac{23}{36},

{t a n}^{- 1} \frac{x - 1}{x - 2} + {t a n}^{- 1} \frac{x + 1}{x + 2} = \frac{π}{4}

{t a n}^{- 1} \frac{x - 1}{x + 1} + {t a n}^{- 1} \frac{2 x - 1}{2 x + 1} = {t a n}^{- 1} \frac{23}{36}

{tan}^{- 1} (\frac{x - 1}{x + 1}) + {tan}^{- 1} (\frac{2 x - 1}{2 x + 1}) = {tan}^{- 1} \frac{23}{36}; x > 1,

x

\frac{3 π}{4}

\frac{8}{31}

(\frac{1 - x}{1 + x}) - \frac{1}{2}

\frac{π}{12}

(\frac{8}{79})

\tan^{- 1} \frac{x}{2} + \tan^{- 1} \frac{x}{3} = \frac{π}{4}, 0 < x < \sqrt{6}

\tan^{- 1} (\frac{x - 2}{x - 4}) + \tan^{- 1} (\frac{x + 2}{x + 4}) = \frac{π}{4}

\tan^{- 1} (2 + x) + \tan^{- 1} (2 - x) = \tan^{- 1} \frac{2}{3}, where x < - \sqrt{3} or, x > \sqrt{3}

\tan^{- 1} \frac{x - 2}{x - 1} + \tan^{- 1} \frac{x + 2}{x + 1} = \frac{π}{4}

Solution of the equation tan ^-1 (x - 1) + tan ^-1 x + tan ^-1 (x+1)=tan ^-1 3x is

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