Trigonometry Examples

$\frac{\cos^{5} (x) \sin (x)}{\sin^{5} (x) \cos (x)}$

Step 1

Cancel the common factor of $\cos^{5} (x)$ and $\cos (x)$ .

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Step 1.1

Factor $\cos (x)$ out of $\cos^{5} (x) \sin (x)$ .

$\frac{\cos (x) (\cos^{4} (x) \sin (x))}{\sin^{5} (x) \cos (x)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $\cos (x)$ out of $\sin^{5} (x) \cos (x)$ .

$\frac{\cos (x) (\cos^{4} (x) \sin (x))}{\cos (x) \sin^{5} (x)}$

Step 1.2.2

Cancel the common factor.

$\frac{\cos (x) (\cos^{4} (x) \sin (x))}{\cos (x) \sin^{5} (x)}$

Step 1.2.3

Rewrite the expression.

$\frac{\cos^{4} (x) \sin (x)}{\sin^{5} (x)}$

Step 2

Cancel the common factor of $\sin (x)$ and $\sin^{5} (x)$ .

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Step 2.1

Factor $\sin (x)$ out of $\cos^{4} (x) \sin (x)$ .

$\frac{\sin (x) \cos^{4} (x)}{\sin^{5} (x)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $\sin (x)$ out of $\sin^{5} (x)$ .

$\frac{\sin (x) \cos^{4} (x)}{\sin (x) \sin^{4} (x)}$

Step 2.2.2

Cancel the common factor.

$\frac{\sin (x) \cos^{4} (x)}{\sin (x) \sin^{4} (x)}$

Step 2.2.3

Rewrite the expression.

$\frac{\cos^{4} (x)}{\sin^{4} (x)}$

Step 3

Convert from $\frac{\cos^{4} (x)}{\sin^{4} (x)}$ to $\cot^{4} (x)$ .

$\cot^{4} (x)$