Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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

Step 2

Since $\cos (- x)$ is an even function, rewrite $\cos (- x)$ as $\cos (x)$ .

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$1$