Trigonometry Examples

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

Step 1

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

$\frac{1}{\cos (x)} \tan (x) \cos (x) \csc (x)$

Step 2

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

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Step 2.1

Add parentheses.

$\frac{1}{\cos (x)} (\tan (x) \cos (x)) \csc (x)$

Step 2.2

Rewrite $\frac{1}{\cos (x)} \tan (x) \cos (x)$ in terms of sines and cosines.

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

Step 2.3

Cancel the common factors.

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

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

$\sec (x)$