Evaluate (tan(pi/4))/2-1/(sec(pi/3))

$\frac{\tan (\frac{π}{4})}{2} - \frac{1}{\sec (\frac{π}{3})}$

Simplify each term.

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

$\frac{1}{2} - \frac{1}{\sec (\frac{π}{3})}$

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

$\frac{1}{2} - \frac{1}{\frac{1}{\cos (\frac{π}{3})}}$

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

$\frac{1}{2} - (1 \cos (\frac{π}{3}))$

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

$\frac{1}{2} - \cos (\frac{π}{3})$

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$\frac{1}{2} - \frac{1}{2}$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{1 - 1}{2}$

Simplify the expression.

Subtract $1$ from $1$ .

$\frac{0}{2}$

Divide $0$ by $2$ .

$0$