Trigonometry Examples

$\frac{\csc (- x)}{\cot (- x)}$

Step 1

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

$\frac{- \csc (x)}{\cot (- x)}$

Step 2

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

$\frac{- \csc (x)}{- \cot (x)}$

Step 3

Dividing two negative values results in a positive value.

$\frac{\csc (x)}{\cot (x)}$

Step 4

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

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

Step 5

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

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

Step 6

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (x)}{\sin (x)}$ .

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

Step 7

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

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

Step 8

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

$\sec (x)$