Trigonometry Examples

$\frac{2 (\frac{7}{24})}{1 - {(\frac{7}{24})}^{2}}$

Step 1

Combine $2$ and $\frac{7}{24}$ .

$\frac{\frac{2 \cdot 7}{24}}{1 - {(\frac{7}{24})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{7}{24}$ .

$\frac{\frac{2 \cdot 7}{24}}{1 - \frac{7^{2}}{24^{2}}}$

Step 2.2

Raise $7$ to the power of $2$ .

$\frac{\frac{2 \cdot 7}{24}}{1 - \frac{49}{24^{2}}}$

Step 2.3

Raise $24$ to the power of $2$ .

$\frac{\frac{2 \cdot 7}{24}}{1 - \frac{49}{576}}$

Step 2.4

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

$\frac{\frac{2 \cdot 7}{24}}{\frac{576}{576} - \frac{49}{576}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 7}{24}}{\frac{576 - 49}{576}}$

Step 2.6

Subtract $49$ from $576$ .

$\frac{\frac{2 \cdot 7}{24}}{\frac{527}{576}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $2$ by $7$ .

$\frac{\frac{14}{24}}{\frac{527}{576}}$

Step 3.2

Cancel the common factor of $14$ and $24$ .

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Step 3.2.1

Factor $2$ out of $14$ .

$\frac{\frac{2 (7)}{24}}{\frac{527}{576}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $24$ .

$\frac{\frac{2 \cdot 7}{2 \cdot 12}}{\frac{527}{576}}$

Step 3.2.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 7}{2 \cdot 12}}{\frac{527}{576}}$

Step 3.2.2.3

Rewrite the expression.

$\frac{\frac{7}{12}}{\frac{527}{576}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{12} \cdot \frac{576}{527}$

Step 5

Cancel the common factor of $12$ .

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Step 5.1

Factor $12$ out of $576$ .

$\frac{7}{12} \cdot \frac{12 (48)}{527}$

Step 5.2

Cancel the common factor.

$\frac{7}{12} \cdot \frac{12 \cdot 48}{527}$

Step 5.3

Rewrite the expression.

$7 (\frac{48}{527})$

Step 6

Combine $7$ and $\frac{48}{527}$ .

$\frac{7 \cdot 48}{527}$

Step 7

Multiply $7$ by $48$ .

$\frac{336}{527}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{336}{527}$

Decimal Form:

$0.63757115 \dots$