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

let

partial fractions

Plug back in for u and x

So far we have

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To integrate tan(x)/(1+cos(x)), you can use the trigonometric substitution method. Let ( u = \tan(\frac{x}{2}) ). Then, ( \cos(x) = \frac{1-u^2}{1+u^2} ) and ( \sin(x) = \frac{2u}{1+u^2} ). Substitute these into the integral, and you'll end up with an integral involving ( u ). After integrating with respect to ( u ), you can then substitute back in terms of ( x ) to get 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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