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∫ √ 1 − Cos X 1 + Cos X D X - Mathematics

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प्रश्न

\[\int\sqrt{\frac{1 - \cos x}{1 + \cos x}} dx\]
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उत्तर

\[\int\sqrt{\frac{1 - \cos x}{1 + \cos x}} dx\]

` ∫   \sqrt {{2 sin^2  x/2} / {2 cos^2   x/2 }}      dx`  `[ ∵ 1 - cos x = 2 sin^2      x/2    & 1 + cos x = 2 cos ^2   x/2]`

\[ = \int\tan\frac{x}{2} dx\]

\[ =\text{ - 2 }\text{ln }\left| \cos\frac{x}{2} \right| + C\]

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अध्याय 19: Indefinite Integrals - Exercise 19.08 [पृष्ठ ४७]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Exercise 19.08 | Q 4 | पृष्ठ ४७

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