# How do you integrate #(1-cosx)/(1+cosx)#?

Just do some basic math first:

We can now factor the numerator as follows:

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To integrate ( \frac{{1 - \cos(x)}}{{1 + \cos(x)}} ), you can use a trigonometric substitution method.

First, let ( u = \tan\left(\frac{x}{2}\right) ), then ( \cos(x) = \frac{1-u^2}{1+u^2} ) and ( dx = \frac{2}{1+u^2} , du ).

Substituting these into the integral, you get:

[ \int \frac{1 - \frac{1-u^2}{1+u^2}}{1 + \frac{1-u^2}{1+u^2}} \cdot \frac{2}{1+u^2} , du ]

Simplify the expression to integrate. Then integrate to find the final result.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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