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Standard Formulae - 3

Evaluate: ∫...

Question

Evaluate: $\int \frac{1 - cos x}{1 + cos x}$

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Solution

We know that $\frac{1 - cos x}{1 + cos x} = {tan}^{2} (x / 2)$
So, $I = \int \frac{1 - cos x}{1 + cos x} d x = \int t a n^{2} (x / 2) d x = \int ({sec}^{2} (x / 2) - 1) d x$
$I = 2 tan (x / 2) - x + c$

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