# How do you simplify the expression #sectheta/tantheta#?

Apply the identity

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To simplify the expression ( \frac{\sec(\theta)}{\tan(\theta)} ), we can use trigonometric identities. First, recall the definitions of secant and tangent:

( \sec(\theta) = \frac{1}{\cos(\theta)} )

( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} )

Substitute these definitions into the expression:

( \frac{\sec(\theta)}{\tan(\theta)} = \frac{\frac{1}{\cos(\theta)}}{\frac{\sin(\theta)}{\cos(\theta)}} )

Now, simplify the expression by multiplying the numerator by the reciprocal of the denominator:

( \frac{\frac{1}{\cos(\theta)}}{\frac{\sin(\theta)}{\cos(\theta)}} = \frac{1}{\cos(\theta)} \times \frac{\cos(\theta)}{\sin(\theta)} )

( = \frac{1}{\sin(\theta)} )

Thus, ( \frac{\sec(\theta)}{\tan(\theta)} = \frac{1}{\sin(\theta)} ), which can also be written as ( \csc(\theta) ).

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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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