Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Rewrite $\frac{\frac{\cos (x)}{\sin (x)}}{\cos (x)}$ as a product.

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

Step 1.3

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

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 1.4

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

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

Step 2

Subtract $\frac{1}{\sin (x)}$ from $\frac{1}{\sin (x)}$ .

$0$