Trigonometry Examples

${(\frac{60}{61})}^{2} - {(\frac{11}{61})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{60}{61}$ .

$\frac{60^{2}}{61^{2}} - {(\frac{11}{61})}^{2}$

Step 1.2

Raise $60$ to the power of $2$ .

$\frac{3600}{61^{2}} - {(\frac{11}{61})}^{2}$

Step 1.3

Raise $61$ to the power of $2$ .

$\frac{3600}{3721} - {(\frac{11}{61})}^{2}$

Step 1.4

Apply the product rule to $\frac{11}{61}$ .

$\frac{3600}{3721} - \frac{11^{2}}{61^{2}}$

Step 1.5

Raise $11$ to the power of $2$ .

$\frac{3600}{3721} - \frac{121}{61^{2}}$

Step 1.6

Raise $61$ to the power of $2$ .

$\frac{3600}{3721} - \frac{121}{3721}$

$\frac{3600}{3721} - \frac{121}{3721}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{3600 - 121}{3721}$

Step 2.2

Subtract $121$ from $3600$ .

$\frac{3479}{3721}$

$\frac{3479}{3721}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3479}{3721}$

Decimal Form:

$0.93496371 \dots$

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