Questions: Find the exact value of the expression. Do not use a calculator
tan (π 5)/4 + tan (5 π)/4
(23+1)/2
(2+2+1)/6
sqrt(3)/2
0
None of these
1/2
Transcript text: Find the exact value of the expression. Do not use a calculator
\[
\tan \frac{\pi 5}{4}+\tan \frac{5 \pi}{4}
\]
$\frac{23+1}{2}$
$\frac{2+2+1}{6}$
$\frac{\sqrt{3}}{2}$
0
None of these
$\frac{1}{2}$
Solution
Solution Steps
Step 1: Evaluate the Angle
We start by evaluating the angle 45π. This angle is located in the third quadrant of the unit circle.
Step 2: Calculate the Tangent
Next, we calculate tan(45π). In the third quadrant, the tangent function is positive, and we find that:
tan(45π)=1
Step 3: Sum the Tangent Values
Since the expression requires us to find tan(45π)+tan(45π), we can sum the two values:
tan(45π)+tan(45π)=1+1=2