Evaluate (tan(pi/3))/2+1/(csc(pi/3))

$\frac{\tan (\frac{π}{3})}{2} + \frac{1}{\csc (\frac{π}{3})}$

Simplify each term.

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

$\frac{\sqrt{3}}{2} + \frac{1}{\csc (\frac{π}{3})}$

Rewrite $\csc (\frac{π}{3})$ in terms of sines and cosines.

$\frac{\sqrt{3}}{2} + \frac{1}{\frac{1}{\sin (\frac{π}{3})}}$

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (\frac{π}{3})}$ .

$\frac{\sqrt{3}}{2} + 1 \sin (\frac{π}{3})$

Multiply $\sin (\frac{π}{3})$ by $1$ .

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

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

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

Simplify terms.

Combine the numerators over the common denominator.

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

Add $\sqrt{3}$ and $\sqrt{3}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $\sqrt{3}$ by $1$ .

$\sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$