# How do you simplify #Tan(x) Csc(x)/sec(x)#?

Simplify:

Ans: 1

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To simplify (\tan(x) \csc(x) / \sec(x)), use trigonometric identities:

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

Substitute these identities into the expression:

[\frac{\tan(x) \csc(x)}{\sec(x)} = \frac{\tan(x) \frac{1}{\sin(x)}}{\frac{1}{\cos(x)}}]

Now, multiply the numerator and denominator by (\sin(x)) to rationalize:

[\frac{\tan(x) \frac{1}{\sin(x)}}{\frac{1}{\cos(x)}} \times \frac{\sin(x)}{\sin(x)} = \frac{\tan(x)}{\frac{\sin(x)}{\cos(x)}}]

Using the identity (\tan(x) = \frac{\sin(x)}{\cos(x)}):

[\frac{\tan(x)}{\frac{\sin(x)}{\cos(x)}} = \frac{\tan(x)}{\tan(x)} = \boxed{1}]

Therefore, (\tan(x) \csc(x) / \sec(x)) simplifies to (1).

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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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