Trigonometry Examples

{(\frac{15}{17})}^{2} - {(\frac{8}{17})}^{2}

${(\frac{15}{17})}^{2} - {(\frac{8}{17})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to

\frac{15}{17}

$\frac{15}{17}$ .

\frac{15^{2}}{17^{2}} - {(\frac{8}{17})}^{2}

$\frac{15^{2}}{17^{2}} - {(\frac{8}{17})}^{2}$

Step 1.2

Raise

15

$15$ to the power of

2

$2$ .

\frac{225}{17^{2}} - {(\frac{8}{17})}^{2}

$\frac{225}{17^{2}} - {(\frac{8}{17})}^{2}$

Step 1.3

Raise

17

$17$ to the power of

2

$2$ .

\frac{225}{289} - {(\frac{8}{17})}^{2}

$\frac{225}{289} - {(\frac{8}{17})}^{2}$

Step 1.4

Apply the product rule to

\frac{8}{17}

$\frac{8}{17}$ .

\frac{225}{289} - \frac{8^{2}}{17^{2}}

$\frac{225}{289} - \frac{8^{2}}{17^{2}}$

Step 1.5

Raise

8

$8$ to the power of

2

$2$ .

\frac{225}{289} - \frac{64}{17^{2}}

$\frac{225}{289} - \frac{64}{17^{2}}$

Step 1.6

Raise

17

$17$ to the power of

2

$2$ .

\frac{225}{289} - \frac{64}{289}

$\frac{225}{289} - \frac{64}{289}$

\frac{225}{289} - \frac{64}{289}

$\frac{225}{289} - \frac{64}{289}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

\frac{225 - 64}{289}

$\frac{225 - 64}{289}$

Step 2.2

Subtract

64

$64$ from

225

$225$ .

\frac{161}{289}

$\frac{161}{289}$

\frac{161}{289}

$\frac{161}{289}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{161}{289}

$\frac{161}{289}$

Decimal Form:

0.55709342 \dots

$0.55709342 \dots$

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

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