Find the Exact Value (tan(pi/4))/2+1/(sec(pi/3))

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

Step 1

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 $\frac{1}{2}$ .

$\frac{1}{2} + \frac{1}{2}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{1 + 1}{2}$

Simplify the expression.

Add $1$ and $1$ .

$\frac{2}{2}$

Divide $2$ by $2$ .

$1$