Find the Exact Value sec(pi/6)tan(pi/6)

$\sec (\frac{π}{6}) \tan (\frac{π}{6})$

The exact value of $\sec (\frac{π}{6})$ is $\frac{2}{\sqrt{3}}$ .

$\frac{2}{\sqrt{3}} \tan (\frac{π}{6})$

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \tan (\frac{π}{6})$

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{2 \sqrt{3}}{\sqrt{3} \sqrt{3}} \tan (\frac{π}{6})$

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{2 \sqrt{3}}{3} \tan (\frac{π}{6})$

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

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

Multiply $\frac{2 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3}$ .

Multiply $\frac{2 \sqrt{3}}{3}$ by $\frac{\sqrt{3}}{3}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{2 {\sqrt{3}}^{2}}{3 \cdot 3}$

Multiply $3$ by $3$ .

$\frac{2 {\sqrt{3}}^{2}}{9}$

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

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

$\frac{2 {(3^{\frac{1}{2}})}^{2}}{9}$

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

$\frac{2 \cdot 3^{\frac{1}{2} \cdot 2}}{9}$

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

$\frac{2 \cdot 3^{\frac{2}{2}}}{9}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 3^{\frac{2}{2}}}{9}$

Rewrite the expression.

$\frac{2 \cdot 3^{1}}{9}$

Evaluate the exponent.

$\frac{2 \cdot 3}{9}$

Multiply $2$ by $3$ .

$\frac{6}{9}$

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6$ .

$\frac{3 (2)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$\frac{3 \cdot 2}{3 \cdot 3}$

Cancel the common factor.

$\frac{3 \cdot 2}{3 \cdot 3}$

Rewrite the expression.

$\frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$

Find the Exact Value sec(pi/6)tan(pi/6)

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