Find the Exact Value 2tan(pi/4)+cos(pi/4)tan(pi/3)

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

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

$2 \cdot 1 + \cos (\frac{π}{4}) \tan (\frac{π}{3})$

Multiply $2$ by $1$ .

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

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

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

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

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

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

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

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

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

$2 + \frac{\sqrt{6}}{2}$

The result can be shown in multiple forms.

Exact Form:

$2 + \frac{\sqrt{6}}{2}$

Decimal Form:

$3.22474487 \dots$