Precalculus Examples

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

Step 1

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

$\sin (x) \cos (x) \frac{\sin (x)}{\cos (x)} \sec (x) \csc (x)$

Step 2

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

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Step 2.1

Factor $\cos (x)$ out of $\sin (x) \cos (x)$ .

$\cos (x) \sin (x) \frac{\sin (x)}{\cos (x)} \sec (x) \csc (x)$

Step 2.2

Cancel the common factor.

$\cos (x) \sin (x) \frac{\sin (x)}{\cos (x)} \sec (x) \csc (x)$

Step 2.3

Rewrite the expression.

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

Step 3

Raise $\sin (x)$ to the power of $1$ .

$\sin^{1} (x) \sin (x) \sec (x) \csc (x)$

Step 4

Raise $\sin (x)$ to the power of $1$ .

$\sin^{1} (x) \sin^{1} (x) \sec (x) \csc (x)$

Step 5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sin (x)}^{1 + 1} \sec (x) \csc (x)$

Step 6

Add $1$ and $1$ .

$\sin^{2} (x) \sec (x) \csc (x)$

Step 7

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

$\sin^{2} (x) \frac{1}{\cos (x)} \csc (x)$

Step 8

Combine $\sin^{2} (x)$ and $\frac{1}{\cos (x)}$ .

$\frac{\sin^{2} (x)}{\cos (x)} \csc (x)$

Step 9

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

$\frac{\sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\sin (x)}$

Step 10

Combine.

$\frac{\sin^{2} (x) \cdot 1}{\cos (x) \sin (x)}$

Step 11

Cancel the common factor of $\sin^{2} (x)$ and $\sin (x)$ .

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Step 11.1

Factor $\sin (x)$ out of $\sin^{2} (x) \cdot 1$ .

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $\sin (x)$ out of $\cos (x) \sin (x)$ .

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

Step 11.2.2

Cancel the common factor.

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

Step 11.2.3

Rewrite the expression.

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

Step 12

Multiply $\sin (x)$ by $1$ .

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

Step 13

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\tan (x)$