Trigonometry Examples

${(\frac{12}{13})}^{2} - {(\frac{5}{13})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{12}{13}$ .

$\frac{12^{2}}{13^{2}} - {(\frac{5}{13})}^{2}$

Step 1.2

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

$\frac{144}{13^{2}} - {(\frac{5}{13})}^{2}$

Step 1.3

Raise $13$ to the power of $2$ .

$\frac{144}{169} - {(\frac{5}{13})}^{2}$

Step 1.4

Apply the product rule to $\frac{5}{13}$ .

$\frac{144}{169} - \frac{5^{2}}{13^{2}}$

Step 1.5

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

$\frac{144}{169} - \frac{25}{13^{2}}$

Step 1.6

Raise $13$ to the power of $2$ .

$\frac{144}{169} - \frac{25}{169}$

$\frac{144}{169} - \frac{25}{169}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{144 - 25}{169}$

Step 2.2

Subtract $25$ from $144$ .

$\frac{119}{169}$

$\frac{119}{169}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{119}{169}$

Decimal Form:

$0.70414201 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$