Find the Exact Value tan(pi/4)^2+2cos((8pi)/3)-sin((13pi)/6)

The exact value of ${\displaystyle \tan \left(\frac{\pi }{4}\right)}$ is ${\displaystyle 1}$.

One to any power is one.

Subtract full rotations of ${\displaystyle 2\pi }$ until the angle is greater than or equal to ${\displaystyle 0}$ and less than ${\displaystyle 2\pi }$.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

The exact value of ${\displaystyle \cos \left(\frac{\pi }{3}\right)}$ is ${\displaystyle \frac{1}{2}}$.

Cancel the common factor of ${\displaystyle 2}$.

Subtract full rotations of ${\displaystyle 2\pi }$ until the angle is greater than or equal to ${\displaystyle 0}$ and less than ${\displaystyle 2\pi }$.

The exact value of ${\displaystyle \sin \left(\frac{\pi }{6}\right)}$ is ${\displaystyle \frac{1}{2}}$.

Write ${\displaystyle 1}$ as a fraction with denominator ${\displaystyle 1}$.

Multiply ${\displaystyle \frac{1}{1}}$ by ${\displaystyle \frac{2}{2}}$.

Multiply ${\displaystyle \frac{1}{1}}$ by ${\displaystyle \frac{2}{2}}$.

Write ${\displaystyle -1}$ as a fraction with denominator ${\displaystyle 1}$.

Multiply ${\displaystyle \frac{-1}{1}}$ by ${\displaystyle \frac{2}{2}}$.

Multiply ${\displaystyle \frac{-1}{1}}$ by ${\displaystyle \frac{2}{2}}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 2}$.

Subtract ${\displaystyle 2}$ from ${\displaystyle 2}$.

Subtract ${\displaystyle 1}$ from ${\displaystyle 0}$.

Move the negative in front of the fraction.