Precalculus Examples

$2 \tan (\frac{π}{4}) + \cos (\frac{π}{6}) \tan (\frac{π}{3})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Multiply $2$ by $1$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

Tap for more steps...

Step 1.5.1

Combine $\frac{\sqrt{3}}{2}$ and $\sqrt{3}$ .

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

Step 1.5.2

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

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

Step 1.5.3

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

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

Step 1.5.4

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

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

Step 1.5.5

Add $1$ and $1$ .

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

Step 1.6

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

Tap for more steps...

Step 1.6.1

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

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

Step 1.6.2

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

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

Step 1.6.3

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

$2 + \frac{3^{\frac{2}{2}}}{2}$

Step 1.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.6.4.1

Cancel the common factor.

$2 + \frac{3^{\frac{2}{2}}}{2}$

Step 1.6.4.2

Rewrite the expression.

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

Step 1.6.5

Evaluate the exponent.

$2 + \frac{3}{2}$

Step 2

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $2$ by $2$ .

$\frac{4 + 3}{2}$

Step 5.2

Add $4$ and $3$ .

$\frac{7}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{2}$

Decimal Form:

$3.5$

Mixed Number Form:

$3 \frac{1}{2}$