# How do you find the antiderivative of #cosx/cscx#?

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Ratnaker M. has given the correct answer. Here are two other ways to get (and to write) the answer.

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To find the antiderivative of (\frac{\cos x}{\csc x}), you can rewrite it in terms of sine and cosine functions. Using the identity (\csc x = \frac{1}{\sin x}), the expression becomes (\frac{\cos x \cdot \sin x}{1}). Then, using the quotient rule for integration, integrate each term separately. The antiderivative of (\cos x \cdot \sin x) can be found using integration by parts. This yields the final result of (-\cos x + C), where (C) is the constant of integration.

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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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