Trigonometry Examples

$\frac{2 (\frac{5}{12})}{1 - {(\frac{5}{12})}^{2}}$

Step 1

Combine $2$ and $\frac{5}{12}$ .

$\frac{\frac{2 \cdot 5}{12}}{1 - {(\frac{5}{12})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{5}{12}$ .

$\frac{\frac{2 \cdot 5}{12}}{1 - \frac{5^{2}}{12^{2}}}$

Step 2.2

Raise $5$ to the power of $2$ .

$\frac{\frac{2 \cdot 5}{12}}{1 - \frac{25}{12^{2}}}$

Step 2.3

Raise $12$ to the power of $2$ .

$\frac{\frac{2 \cdot 5}{12}}{1 - \frac{25}{144}}$

Step 2.4

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

$\frac{\frac{2 \cdot 5}{12}}{\frac{144}{144} - \frac{25}{144}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 5}{12}}{\frac{144 - 25}{144}}$

Step 2.6

Subtract $25$ from $144$ .

$\frac{\frac{2 \cdot 5}{12}}{\frac{119}{144}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $2$ by $5$ .

$\frac{\frac{10}{12}}{\frac{119}{144}}$

Step 3.2

Cancel the common factor of $10$ and $12$ .

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Step 3.2.1

Factor $2$ out of $10$ .

$\frac{\frac{2 (5)}{12}}{\frac{119}{144}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $12$ .

$\frac{\frac{2 \cdot 5}{2 \cdot 6}}{\frac{119}{144}}$

Step 3.2.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 5}{2 \cdot 6}}{\frac{119}{144}}$

Step 3.2.2.3

Rewrite the expression.

$\frac{\frac{5}{6}}{\frac{119}{144}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{6} \cdot \frac{144}{119}$

Step 5

Cancel the common factor of $6$ .

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Step 5.1

Factor $6$ out of $144$ .

$\frac{5}{6} \cdot \frac{6 (24)}{119}$

Step 5.2

Cancel the common factor.

$\frac{5}{6} \cdot \frac{6 \cdot 24}{119}$

Step 5.3

Rewrite the expression.

$5 (\frac{24}{119})$

Step 6

Combine $5$ and $\frac{24}{119}$ .

$\frac{5 \cdot 24}{119}$

Step 7

Multiply $5$ by $24$ .

$\frac{120}{119}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{120}{119}$

Decimal Form:

$1.00840336 \dots$

Mixed Number Form:

$1 \frac{1}{119}$