Find the Exact Value tan(pi/12)

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Trigonometry

$\tan (\frac{π}{12})$

Split $\frac{π}{12}$ into two angles where the values of the six trigonometric functions are known.

$\tan (\frac{π}{4} - \frac{π}{6})$

Apply the difference of angles identity.

$\frac{\tan (\frac{π}{4}) - \tan (\frac{π}{6})}{1 + \tan (\frac{π}{4}) \tan (\frac{π}{6})}$

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\frac{1 - \tan (\frac{π}{6})}{1 + \tan (\frac{π}{4}) \tan (\frac{π}{6})}$

The exact value of $\tan (\frac{π}{6})$ is $\frac{\sqrt{3}}{3}$ .

$\frac{1 - \frac{\sqrt{3}}{3}}{1 + \tan (\frac{π}{4}) \tan (\frac{π}{6})}$

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\frac{1 - \frac{\sqrt{3}}{3}}{1 + 1 \tan (\frac{π}{6})}$

The exact value of $\tan (\frac{π}{6})$ is $\frac{\sqrt{3}}{3}$ .

$\frac{1 - \frac{\sqrt{3}}{3}}{1 + 1 \frac{\sqrt{3}}{3}}$

Simplify $\frac{1 - \frac{\sqrt{3}}{3}}{1 + 1 \frac{\sqrt{3}}{3}}$ .

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Multiply the numerator and denominator of the complex fraction by $3$ .

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Multiply $\frac{1 - \frac{\sqrt{3}}{3}}{1 + 1 \frac{\sqrt{3}}{3}}$ by $\frac{3}{3}$ .

$\frac{3}{3} \cdot \frac{1 - \frac{\sqrt{3}}{3}}{1 + 1 \frac{\sqrt{3}}{3}}$

Combine.

$\frac{3 (1 - \frac{\sqrt{3}}{3})}{3 (1 + 1 \frac{\sqrt{3}}{3})}$

Apply the distributive property.

$\frac{3 \cdot 1 + 3 (- \frac{\sqrt{3}}{3})}{3 \cdot 1 + 3 (1 \frac{\sqrt{3}}{3})}$

Cancel the common factor of $3$ .

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Move the leading negative in $- \frac{\sqrt{3}}{3}$ into the numerator.

$\frac{3 \cdot 1 + 3 \frac{- \sqrt{3}}{3}}{3 \cdot 1 + 3 (1 \frac{\sqrt{3}}{3})}$

Cancel the common factor.

$\frac{3 \cdot 1 + 3 \frac{- \sqrt{3}}{3}}{3 \cdot 1 + 3 (1 \frac{\sqrt{3}}{3})}$

Rewrite the expression.

$\frac{3 \cdot 1 - \sqrt{3}}{3 \cdot 1 + 3 (1 \frac{\sqrt{3}}{3})}$

Multiply $3$ by $1$ .

$\frac{3 - \sqrt{3}}{3 \cdot 1 + 3 (1 \frac{\sqrt{3}}{3})}$

Simplify the denominator.

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Multiply $3$ by $1$ .

$\frac{3 - \sqrt{3}}{3 + 3 (1 \frac{\sqrt{3}}{3})}$

Multiply $\frac{\sqrt{3}}{3}$ by $1$ .

$\frac{3 - \sqrt{3}}{3 + 3 \frac{\sqrt{3}}{3}}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 - \sqrt{3}}{3 + 3 \frac{\sqrt{3}}{3}}$

Rewrite the expression.

$\frac{3 - \sqrt{3}}{3 + \sqrt{3}}$

Multiply $\frac{3 - \sqrt{3}}{3 + \sqrt{3}}$ by $\frac{3 - \sqrt{3}}{3 - \sqrt{3}}$ .

$\frac{3 - \sqrt{3}}{3 + \sqrt{3}} \cdot \frac{3 - \sqrt{3}}{3 - \sqrt{3}}$

Multiply $\frac{3 - \sqrt{3}}{3 + \sqrt{3}}$ and $\frac{3 - \sqrt{3}}{3 - \sqrt{3}}$ .

$\frac{(3 - \sqrt{3}) (3 - \sqrt{3})}{(3 + \sqrt{3}) (3 - \sqrt{3})}$

Expand the denominator using the FOIL method.

$\frac{(3 - \sqrt{3}) (3 - \sqrt{3})}{9 - 3 \sqrt{3} + \sqrt{3} \cdot 3 - {\sqrt{3}}^{2}}$

Simplify.

$\frac{(3 - \sqrt{3}) (3 - \sqrt{3})}{6}$

Simplify the numerator.

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Raise $3 - \sqrt{3}$ to the power of $1$ .

$\frac{{(3 - \sqrt{3})}^{1} (3 - \sqrt{3})}{6}$

Raise $3 - \sqrt{3}$ to the power of $1$ .

$\frac{{(3 - \sqrt{3})}^{1} {(3 - \sqrt{3})}^{1}}{6}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(3 - \sqrt{3})}^{1 + 1}}{6}$

Add $1$ and $1$ .

$\frac{{(3 - \sqrt{3})}^{2}}{6}$

Rewrite ${(3 - \sqrt{3})}^{2}$ as $(3 - \sqrt{3}) (3 - \sqrt{3})$ .

$\frac{(3 - \sqrt{3}) (3 - \sqrt{3})}{6}$

Expand $(3 - \sqrt{3}) (3 - \sqrt{3})$ using the FOIL Method.

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Apply the distributive property.

$\frac{3 (3 - \sqrt{3}) - \sqrt{3} (3 - \sqrt{3})}{6}$

Apply the distributive property.

$\frac{3 \cdot 3 + 3 (- \sqrt{3}) - \sqrt{3} (3 - \sqrt{3})}{6}$

Apply the distributive property.

$\frac{3 \cdot 3 + 3 (- \sqrt{3}) - \sqrt{3} \cdot 3 - \sqrt{3} (- \sqrt{3})}{6}$

Simplify and combine like terms.

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Simplify each term.

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Multiply $3$ by $3$ .

$\frac{9 + 3 (- \sqrt{3}) - \sqrt{3} \cdot 3 - \sqrt{3} (- \sqrt{3})}{6}$

Multiply $- 1$ by $3$ .

$\frac{9 - 3 \sqrt{3} - \sqrt{3} \cdot 3 - \sqrt{3} (- \sqrt{3})}{6}$

Multiply $3$ by $- 1$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} - \sqrt{3} (- \sqrt{3})}{6}$

Multiply $- \sqrt{3} (- \sqrt{3})$ .

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Multiply $- 1$ by $- 1$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + 1 \sqrt{3} \sqrt{3}}{6}$

Multiply $\sqrt{3}$ by $1$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + \sqrt{3} \sqrt{3}}{6}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + {\sqrt{3}}^{1} \sqrt{3}}{6}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + {\sqrt{3}}^{1} {\sqrt{3}}^{1}}{6}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + {\sqrt{3}}^{1 + 1}}{6}$

Add $1$ and $1$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + {\sqrt{3}}^{2}}{6}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + {(3^{\frac{1}{2}})}^{2}}{6}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + 3^{\frac{1}{2} \cdot 2}}{6}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + 3^{\frac{2}{2}}}{6}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + 3^{\frac{2}{2}}}{6}$

Divide $1$ by $1$ .

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + 3^{1}}{6}$

Evaluate the exponent.

$\frac{9 - 3 \sqrt{3} - 3 \sqrt{3} + 3}{6}$

Add $9$ and $3$ .

$\frac{12 - 3 \sqrt{3} - 3 \sqrt{3}}{6}$

Subtract $3 \sqrt{3}$ from $- 3 \sqrt{3}$ .

$\frac{12 - 6 \sqrt{3}}{6}$

Cancel the common factor of $12 - 6 \sqrt{3}$ and $6$ .

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Factor $6$ out of $12$ .

$\frac{6 \cdot 2 - 6 \sqrt{3}}{6}$

Factor $6$ out of $- 6 \sqrt{3}$ .

$\frac{6 \cdot 2 + 6 (- \sqrt{3})}{6}$

Factor $6$ out of $6 (2) + 6 (- \sqrt{3})$ .

$\frac{6 (2 - \sqrt{3})}{6}$

Cancel the common factors.

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Factor $6$ out of $6$ .

$\frac{6 (2 - \sqrt{3})}{6 (1)}$

Cancel the common factor.

$\frac{6 (2 - \sqrt{3})}{6 \cdot 1}$

Rewrite the expression.

$\frac{2 - \sqrt{3}}{1}$

Divide $2 - \sqrt{3}$ by $1$ .

$2 - \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$2 - \sqrt{3}$

Decimal Form:

$0.26794919 \dots$

Do you know how to Find the Exact Value tan(pi/12)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	five hundred sixty-seven million one hundred fifty-seven thousand nine hundred thirteen

Interesting facts

567157913 has 4 divisors, whose sum is 648180480
The reverse of 567157913 is 319751765
Previous prime number is 7

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 44
Digital Root 8

Name

Name	one billion six hundred thirty-three million one hundred thirty-six thousand six hundred ninety

Interesting facts

1633136690 has 8 divisors, whose sum is 2939646060
The reverse of 1633136690 is 0966313361
Previous prime number is 5

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 38
Digital Root 2

Name

Name	two hundred seven million seven hundred ninety-six thousand four hundred thirty-two

Interesting facts

207796432 has 64 divisors, whose sum is 1056581820
The reverse of 207796432 is 234697702
Previous prime number is 229

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 40
Digital Root 4

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