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प्रश्न
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
बेरीज
उत्तर
\[\int\left( \frac{1 - \cos x}{1 + \cos x} \right) dx\]
`= ∫ ( {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]`
\[ = \int \tan^2 \frac{x}{2} dx\]
\[ = \int\left( \sec^2 \frac{x}{2} - 1 \right) dx\]
\[ = \frac{\tan \frac{x}{2}}{\frac{1}{2}} - x + C\]
\[ = 2 \tan \frac{x}{2} - x + C\]
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