Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{\cos (x) \sin (x)}{\sin (x)}$ by cancelling the common factors.

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

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

Step 4.2

Divide $\cos (x)$ by $1$ .

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

Step 5

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

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