Evaluate 2sin(pi/3)-3tan(pi/6)

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

Step 1

Simplify each term.

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{3} - 3 \tan (\frac{π}{6})$

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

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

$\sqrt{3} - \sqrt{3}$

Step 2

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

$0$