Find the Exact Value sin(pi/3)cos(pi/4)-tan(pi/3)

$\sin (\frac{π}{3}) \cos (\frac{π}{4}) - \tan (\frac{π}{3})$

Step 1

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

$\frac{\sqrt{3}}{2} \cos (\frac{π}{4}) - \tan (\frac{π}{3})$

Step 2

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

Step 3

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

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

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

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

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

Multiply $2$ by $2$ .

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

Step 4

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

$\frac{\sqrt{6}}{4} - \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6}}{4} - \sqrt{3}$

Decimal Form:

$- 1.11967837 \dots$