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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$\frac{\sqrt{6}}{2 \cdot 2} - \tan (\frac{π}{4})$

Multiply $2$ by $2$ .

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

Step 4

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

$\frac{\sqrt{6}}{4} - 1 \cdot 1$

Step 5

Multiply $- 1$ by $1$ .

$\frac{\sqrt{6}}{4} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6}}{4} - 1$

Decimal Form:

$- 0.38762756 \dots$