Solve - cosec-11 - x22x - tan-11 - x22x - x2

^ 1 ( 1+x^22x )+tan^ 1 ( 1 x^22x )=x2 2tan^ 1x+tan^ 1 ( 1 x^22x )=x2 tan^ 1x+tan^ 1x+tan^ 1 ( 1 x^22x )=x2 tan^ 1 ( 2x1 x^2 )+tan^ 1 ( 1 x^2 ...

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Basic Inverse Trigonometric Functions

Solve : cos...

Question

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

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\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}

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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

x \in (0, 1)

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

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