Trigonometry Examples

$\frac{2 (\frac{1}{9})}{1 - {(\frac{1}{9})}^{2}}$

Step 1

Combine $2$ and $\frac{1}{9}$ .

$\frac{\frac{2}{9}}{1 - {(\frac{1}{9})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{1}{9}$ .

$\frac{\frac{2}{9}}{1 - \frac{1^{2}}{9^{2}}}$

Step 2.2

One to any power is one.

$\frac{\frac{2}{9}}{1 - \frac{1}{9^{2}}}$

Step 2.3

Raise $9$ to the power of $2$ .

$\frac{\frac{2}{9}}{1 - \frac{1}{81}}$

Step 2.4

Write $1$ as a fraction with a common denominator.

$\frac{\frac{2}{9}}{\frac{81}{81} - \frac{1}{81}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{\frac{2}{9}}{\frac{81 - 1}{81}}$

Step 2.6

Subtract $1$ from $81$ .

$\frac{\frac{2}{9}}{\frac{80}{81}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{9} \cdot \frac{81}{80}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $80$ .

$\frac{2}{9} \cdot \frac{81}{2 (40)}$

Step 4.2

Cancel the common factor.

$\frac{2}{9} \cdot \frac{81}{2 \cdot 40}$

Step 4.3

Rewrite the expression.

$\frac{1}{9} \cdot \frac{81}{40}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Factor $9$ out of $81$ .

$\frac{1}{9} \cdot \frac{9 (9)}{40}$

Step 5.2

Cancel the common factor.

$\frac{1}{9} \cdot \frac{9 \cdot 9}{40}$

Step 5.3

Rewrite the expression.

$\frac{9}{40}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{40}$

Decimal Form:

$0.225$