Trigonometry Examples

$\frac{\cos^{2} (x) \sin (x)}{\sin^{2} (x) \cos (x)}$

Step 1

Cancel the common factor of $\cos^{2} (x)$ and $\cos (x)$ .

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Step 1.1

Factor $\cos (x)$ out of $\cos^{2} (x) \sin (x)$ .

$\frac{\cos (x) (\cos (x) \sin (x))}{\sin^{2} (x) \cos (x)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $\cos (x)$ out of $\sin^{2} (x) \cos (x)$ .

$\frac{\cos (x) (\cos (x) \sin (x))}{\cos (x) \sin^{2} (x)}$

Step 1.2.2

Cancel the common factor.

$\frac{\cos (x) (\cos (x) \sin (x))}{\cos (x) \sin^{2} (x)}$

Step 1.2.3

Rewrite the expression.

$\frac{\cos (x) \sin (x)}{\sin^{2} (x)}$

Step 2

Cancel the common factor of $\sin (x)$ and $\sin^{2} (x)$ .

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Step 2.1

Factor $\sin (x)$ out of $\cos (x) \sin (x)$ .

$\frac{\sin (x) \cos (x)}{\sin^{2} (x)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

$\cot (x)$