Algebra Examples

$\frac{\sin^{3} (θ)}{\tan (θ) - \sin (θ)}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $\tan (θ)$ in terms of sines and cosines.

$\frac{\sin^{3} (θ)}{\frac{\sin (θ)}{\cos (θ)} - \sin (θ)}$

Step 1.2

Factor $\sin (θ)$ out of $\frac{\sin (θ)}{\cos (θ)} - \sin (θ)$ .

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Step 1.2.1

Factor $\sin (θ)$ out of $\frac{\sin (θ)}{\cos (θ)}$ .

$\frac{\sin^{3} (θ)}{\sin (θ) \frac{1}{\cos (θ)} - \sin (θ)}$

Step 1.2.2

Factor $\sin (θ)$ out of $- \sin (θ)$ .

$\frac{\sin^{3} (θ)}{\sin (θ) \frac{1}{\cos (θ)} + \sin (θ) \cdot - 1}$

Step 1.2.3

Factor $\sin (θ)$ out of $\sin (θ) \frac{1}{\cos (θ)} + \sin (θ) \cdot - 1$ .

$\frac{\sin^{3} (θ)}{\sin (θ) (\frac{1}{\cos (θ)} - 1)}$

Step 2

Cancel the common factor of $\sin^{3} (θ)$ and $\sin (θ)$ .

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Step 2.1

Factor $\sin (θ)$ out of $\sin^{3} (θ)$ .

$\frac{\sin (θ) \sin^{2} (θ)}{\sin (θ) (\frac{1}{\cos (θ)} - 1)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Cancel the common factor.

$\frac{\sin (θ) \sin^{2} (θ)}{\sin (θ) (\frac{1}{\cos (θ)} - 1)}$

Step 2.2.2

Rewrite the expression.

$\frac{\sin^{2} (θ)}{\frac{1}{\cos (θ)} - 1}$

Step 3

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

$\frac{\sin^{2} (θ)}{\sec (θ) - 1}$