48. tan inverse {1+sinx + 1-sinx ÷ 1+sinx -1-sinx} 0

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{tan}^{- 1} (\frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}})

y = {tan}^{- 1} (\frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}})

x

(1)

0 < x < \frac{π}{2}

(2)

\frac{π}{2} < x < π

\frac{d y}{d x} i f y = {tan}^{- 1} [\frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}}]

{cot}^{- 1} (\frac{\sqrt{1 - sin x} + \sqrt{1 + sin x}}{\sqrt{1 - sin x} - \sqrt{1 + sin x}})

(0 < x < \frac{π}{2})

{cot}^{- 1} (\frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}}) = \frac{x}{2}, x \in (0, \frac{π}{4})

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