Find the exact value of the expression. Do not use a calculator.
-$$\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }$$
A) 0
B) $\frac { 1 } { 2 }$
C) $\frac { \sqrt { 2 } + 1 } { 2 }$
D) $\frac { 2 \sqrt { 2 } + 1 } { 6 }$

Question

Quizplus · Accepted Answer

The angles $\frac{7\pi}{4}$ and $\frac{5\pi}{4}$ are both in the fourth and third quadrants respectively, where the tangent function is positive in the third quadrant and negative in the fourth. Both angles reference the 45-degree angle ($\frac{\pi}{4}$) in their respective quadrants. Thus, $\tan(\frac{7\pi}{4}) = \tan(360^\circ - 45^\circ) = \tan(-45^\circ) = -1$ and $\tan(\frac{5\pi}{4}) = \tan(180^\circ + 45^\circ) = \tan(225^\circ) = 1$. Adding these values, $-1 + 1 = 0$.

Find the Exact Value of the Expression tan⁡7π4+tan⁡5π4\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }tan47π​+tan45π​

Find the Exact Value of the Expression $\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }$