Precalculus Examples

$\tan (x) (\cot (x) - \csc (x))$

Step 1

Apply the distributive property.

$\tan (x) \cot (x) + \tan (x) (- \csc (x))$

Step 2

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 2.1

Reorder $\tan (x)$ and $\cot (x)$ .

$\cot (x) \tan (x) + \tan (x) (- \csc (x))$

Step 2.2

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

$\frac{\cos (x)}{\sin (x)} \cdot \frac{\sin (x)}{\cos (x)} + \tan (x) (- \csc (x))$

Step 2.3

Cancel the common factors.

$1 + \tan (x) (- \csc (x))$

Step 3

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 3.1

Reorder $\tan (x)$ and $- \csc (x)$ .

$1 - \csc (x) \tan (x)$

Step 3.2

Add parentheses.

$1 - (\csc (x) \tan (x))$

Step 3.3

Reorder $\csc (x)$ and $\tan (x)$ .

$1 - (\tan (x) \csc (x))$

Step 3.4

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

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

Step 3.5

Cancel the common factors.

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

Step 4

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$1 - \sec (x)$