# How do you solve: csc(-x)/sec(-x) ?

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To solve ( \csc(-x)/\sec(-x) ), we first need to understand the reciprocal trigonometric functions.

The reciprocal of sine is cosecant, and the reciprocal of cosine is secant. So, ( \csc(-x) ) is the reciprocal of sine of (-x), and ( \sec(-x) ) is the reciprocal of cosine of (-x).

Using the even and odd properties of trigonometric functions, we can simplify ( \csc(-x)/\sec(-x) ) as follows:

- ( \csc(-x) = \frac{1}{\sin(-x)} = -\frac{1}{\sin(x)} ) because sine is an odd function.
- ( \sec(-x) = \frac{1}{\cos(-x)} = \frac{1}{\cos(x)} ) because cosine is an even function.

So, ( \frac{\csc(-x)}{\sec(-x)} = \frac{-\frac{1}{\sin(x)}}{\frac{1}{\cos(x)}} = -\frac{\cos(x)}{\sin(x)} ).

Therefore, ( \frac{\csc(-x)}{\sec(-x)} = -\cot(x) ).

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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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