Solve - tan-11-x1-x-12tan-1x

Let x=tantSo, [ tan ^ 1( 1 tan t/1 + tan t) = 1/2tan ^ 1( tan t); tan ^ 1( tan( π/4) tan t/1 + tan( π/4) ×tan t) = 1/2tan ^ 1 ...

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Homogeneous Differential Equation

Solve : tan-...

Question

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

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{tan}^{- 1} \frac{1 - x}{1 + x} = \frac{1}{2} {tan}^{- 1} x, (x > 0)

{tan}^{- 1} (\frac{1 - x}{1 + x}) = \frac{1}{2} {tan}^{- 1} x, (0 < x < 1)

x

{tan}^{- 1} (\frac{1 - x}{1 + x}) = \frac{1}{2} {tan}^{- 1} x, x > 0

Solve the following equation for x:

$t a n^{- 1} \frac{1 - x}{1 + x} = \frac{1}{2} t a n^{- 1} x, (x > 0)$ .

\tan^{- 1} \frac{1}{4} + 2 \tan^{- 1} \frac{1}{5} + \tan^{- 1} \frac{1}{6} + \tan^{- 1} \frac{1}{x} = \frac{π}{4}

3 \sin^{- 1} \frac{2 x}{1 + x^{2}} - 4 \cos^{- 1} \frac{1 - x^{2}}{1 + x^{2}} + 2 \tan^{- 1} \frac{2 x}{1 - x^{2}} = \frac{π}{3}

\tan^{- 1} (\frac{2 x}{1 - x^{2}}) + \cot^{- 1} (\frac{1 - x^{2}}{2 x}) = \frac{2 π}{3}, x > 0

\tan^{- 1}

\sin

x

=

\tan

\sin

x

x \neq \frac{π}{2}

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

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

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