Trigonometry Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

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

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

Step 3

Add $- \cos (x)$ and $\cos (x)$ .

$\frac{0}{\sin (- x)}$

Step 4

Separate fractions.

$\frac{0}{1} \cdot \frac{1}{\sin (- x)}$

Step 5

Convert from $\frac{1}{\sin (- x)}$ to $\csc (- x)$ .

$\frac{0}{1} \csc (- x)$

Step 6

Divide $0$ by $1$ .

$0 \csc (- x)$

Step 7

Since $\csc (- x)$ is an odd function, rewrite $\csc (- x)$ as $- \csc (x)$ .

$0 (- \csc (x))$

Step 8

Multiply $0 (- \csc (x))$ .

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Step 8.1

Multiply $- 1$ by $0$ .

$0 \csc (x)$

Step 8.2

Multiply $0$ by $\csc (x)$ .

$0$