Precalculus Examples

$(\sec (x) - \csc (x)) \sin (x) \cos (x)$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sec (x)$ in terms of sines and cosines.

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

Step 1.2

Rewrite $\csc (x)$ in terms of sines and cosines.

$(\frac{1}{\cos (x)} - \frac{1}{\sin (x)}) \sin (x) \cos (x)$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$(\frac{1}{\cos (x)} \sin (x) - \frac{1}{\sin (x)} \sin (x)) \cos (x)$

Step 2.2

Combine $\frac{1}{\cos (x)}$ and $\sin (x)$ .

$(\frac{\sin (x)}{\cos (x)} - \frac{1}{\sin (x)} \sin (x)) \cos (x)$

Step 2.3

Cancel the common factor of $\sin (x)$ .

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Step 2.3.1

Move the leading negative in $- \frac{1}{\sin (x)}$ into the numerator.

$(\frac{\sin (x)}{\cos (x)} + \frac{- 1}{\sin (x)} \sin (x)) \cos (x)$

Step 2.3.2

Cancel the common factor.

$(\frac{\sin (x)}{\cos (x)} + \frac{- 1}{\sin (x)} \sin (x)) \cos (x)$

Step 2.3.3

Rewrite the expression.

$(\frac{\sin (x)}{\cos (x)} - 1) \cos (x)$

Step 2.4

Apply the distributive property.

$\frac{\sin (x)}{\cos (x)} \cos (x) - 1 \cos (x)$

Step 2.5

Cancel the common factor of $\cos (x)$ .

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Step 2.5.1

Cancel the common factor.

$\frac{\sin (x)}{\cos (x)} \cos (x) - 1 \cos (x)$

Step 2.5.2

Rewrite the expression.

$\sin (x) - 1 \cos (x)$

Step 2.6

Rewrite $- 1 \cos (x)$ as $- \cos (x)$ .

$\sin (x) - \cos (x)$