Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

Combine $\sqrt{3}$ and $\frac{\sqrt{3}}{3}$ .

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

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.3.4

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

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

Step 1.3.5

Add $1$ and $1$ .

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

Step 1.4

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

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Step 1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{\tan (\frac{π}{6}) + \tan (\frac{π}{3})}{1 - \frac{{(3^{\frac{1}{2}})}^{2}}{3}}$

Step 1.4.2

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

$\frac{\tan (\frac{π}{6}) + \tan (\frac{π}{3})}{1 - \frac{3^{\frac{1}{2} \cdot 2}}{3}}$

Step 1.4.3

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

$\frac{\tan (\frac{π}{6}) + \tan (\frac{π}{3})}{1 - \frac{3^{\frac{2}{2}}}{3}}$

Step 1.4.4

Cancel the common factor of $2$ .

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Step 1.4.4.1

Cancel the common factor.

$\frac{\tan (\frac{π}{6}) + \tan (\frac{π}{3})}{1 - \frac{3^{\frac{2}{2}}}{3}}$

Step 1.4.4.2

Rewrite the expression.

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

Step 1.4.5

Evaluate the exponent.

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

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Cancel the common factor.

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

Step 1.5.2

Rewrite the expression.

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

Step 1.6

Multiply $- 1$ by $1$ .

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

Step 2

Subtract $1$ from $1$ .

$\frac{\tan (\frac{π}{6}) + \tan (\frac{π}{3})}{0}$

Step 3

The expression contains a division by $0$ . The expression is undefined.

Undefined