Solve tan-1 -1- cos x1- cos x- 0 - x - -

tan^ 1 (√(1 cos x1+cos x)) =tan^ 1 (√(tan^2 x2)) =tan^ 1 (tanx2) =x2 ...

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Basic Trigonometric Identities

Solve tan-1...

Question

Solve
${tan}^{- 1} (\sqrt{\frac{1 - cos x}{1 + cos x}}), 0 < x < π$

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

π < x < \frac{3 π}{2}

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

π < x < \frac{3 π}{2}

{tan}^{- 1} (\begin{matrix} \sqrt{\frac{1 - cos x}{1 + cos x}} \end{matrix}) 0 < x < π .

\frac{d y}{d x}

y = {tan}^{- 1} {\sqrt{\frac{1 + cos x}{1 - cos x}}}

0 < x < π

\frac{d y}{d x}

y = {tan}^{- 1} {\sqrt{\frac{1 + cos x}{1 - cos x}}}

0 < x < π

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