Trigonometry Examples

$\frac{2 (\frac{8}{15})}{1 - {(\frac{8}{15})}^{2}}$

Step 1

Combine $2$ and $\frac{8}{15}$ .

$\frac{\frac{2 \cdot 8}{15}}{1 - {(\frac{8}{15})}^{2}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $\frac{8}{15}$ .

$\frac{\frac{2 \cdot 8}{15}}{1 - \frac{8^{2}}{15^{2}}}$

Step 2.2

Raise $8$ to the power of $2$ .

$\frac{\frac{2 \cdot 8}{15}}{1 - \frac{64}{15^{2}}}$

Step 2.3

Raise $15$ to the power of $2$ .

$\frac{\frac{2 \cdot 8}{15}}{1 - \frac{64}{225}}$

Step 2.4

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

$\frac{\frac{2 \cdot 8}{15}}{\frac{225}{225} - \frac{64}{225}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 8}{15}}{\frac{225 - 64}{225}}$

Step 2.6

Subtract $64$ from $225$ .

$\frac{\frac{2 \cdot 8}{15}}{\frac{161}{225}}$

Step 3

Multiply $2$ by $8$ .

$\frac{\frac{16}{15}}{\frac{161}{225}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{16}{15} \cdot \frac{225}{161}$

Step 5

Cancel the common factor of $15$ .

Tap for more steps...

Step 5.1

Factor $15$ out of $225$ .

$\frac{16}{15} \cdot \frac{15 (15)}{161}$

Step 5.2

Cancel the common factor.

$\frac{16}{15} \cdot \frac{15 \cdot 15}{161}$

Step 5.3

Rewrite the expression.

$16 (\frac{15}{161})$

Step 6

Combine $16$ and $\frac{15}{161}$ .

$\frac{16 \cdot 15}{161}$

Step 7

Multiply $16$ by $15$ .

$\frac{240}{161}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{240}{161}$

Decimal Form:

$1.49068322 \dots$

Mixed Number Form:

$1 \frac{79}{161}$