Trigonometry Examples

- v \frac{1 + \frac{21}{29}}{1 - \frac{21}{29}}

$- v \frac{1 + \frac{21}{29}}{1 - \frac{21}{29}}$

Step 1

Simplify the numerator.

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Step 1.1

Write

1

$1$ as a fraction with a common denominator.

- v \frac{\frac{29}{29} + \frac{21}{29}}{1 - \frac{21}{29}}

$- v \frac{\frac{29}{29} + \frac{21}{29}}{1 - \frac{21}{29}}$

Step 1.2

Combine the numerators over the common denominator.

- v \frac{\frac{29 + 21}{29}}{1 - \frac{21}{29}}

$- v \frac{\frac{29 + 21}{29}}{1 - \frac{21}{29}}$

Step 1.3

Add

29

$29$ and

21

$21$ .

- v \frac{\frac{50}{29}}{1 - \frac{21}{29}}

$- v \frac{\frac{50}{29}}{1 - \frac{21}{29}}$

- v \frac{\frac{50}{29}}{1 - \frac{21}{29}}

$- v \frac{\frac{50}{29}}{1 - \frac{21}{29}}$

Step 2

Simplify the denominator.

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Step 2.1

Write

1

$1$ as a fraction with a common denominator.

- v \frac{\frac{50}{29}}{\frac{29}{29} - \frac{21}{29}}

$- v \frac{\frac{50}{29}}{\frac{29}{29} - \frac{21}{29}}$

Step 2.2

Combine the numerators over the common denominator.

- v \frac{\frac{50}{29}}{\frac{29 - 21}{29}}

$- v \frac{\frac{50}{29}}{\frac{29 - 21}{29}}$

Step 2.3

Subtract

21

$21$ from

29

$29$ .

- v \frac{\frac{50}{29}}{\frac{8}{29}}

$- v \frac{\frac{50}{29}}{\frac{8}{29}}$

- v \frac{\frac{50}{29}}{\frac{8}{29}}

$- v \frac{\frac{50}{29}}{\frac{8}{29}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

- v (\frac{50}{29} \cdot \frac{29}{8})

$- v (\frac{50}{29} \cdot \frac{29}{8})$

Step 4

Cancel the common factor of

2

$2$ .

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Step 4.1

Factor

2

$2$ out of

50

$50$ .

- v (\frac{2 (25)}{29} \cdot \frac{29}{8})

$- v (\frac{2 (25)}{29} \cdot \frac{29}{8})$

Step 4.2

Factor

2

$2$ out of

8

$8$ .

- v (\frac{2 \cdot 25}{29} \cdot \frac{29}{2 \cdot 4})

$- v (\frac{2 \cdot 25}{29} \cdot \frac{29}{2 \cdot 4})$

Step 4.3

Cancel the common factor.

$- v (\frac{2 \cdot 25}{29} \cdot \frac{29}{2 \cdot 4})$

Step 4.4

Rewrite the expression.

$- v (\frac{25}{29} \cdot \frac{29}{4})$

Step 5

Cancel the common factor of

$29$ .

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Step 5.1

Cancel the common factor.

$- v (\frac{25}{29} \cdot \frac{29}{4})$

Step 5.2

Rewrite the expression.

$- v (25 (\frac{1}{4}))$

Step 6

Combine

$25$ and

$\frac{1}{4}$ .

$- v \frac{25}{4}$

Step 7

Combine

$\frac{25}{4}$ and

$v$ .

$- \frac{25 v}{4}$