Answer:
![Hi, ~I'm ~beinggreat78,~ and~ am~ here~ to~ help~ you.](https://tex.z-dn.net/?f=Hi%2C%20~I%27m%20~beinggreat78%2C~%20and~%20am~%20here~%20to~%20help~%20you.)
The answer is D. Tanɵ. But why? Let's break it down. Tan pi + theta in the base equation should look like this...
![\frac{tan\pi+ tanTheta}{1 - tan\pi * tanTheta}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%5Cpi%2B%20tanTheta%7D%7B1%20-%20tan%5Cpi%20%2A%20tanTheta%7D)
We now have to simplify this expression. Let's do that.
![tan(\pi) = \frac{sin\pi }{cos\pi } = \frac{0}{-1} = 0](https://tex.z-dn.net/?f=tan%28%5Cpi%29%20%3D%20%5Cfrac%7Bsin%5Cpi%20%7D%7Bcos%5Cpi%20%7D%20%3D%20%5Cfrac%7B0%7D%7B-1%7D%20%3D%200)
Now that we have broken this problem into simpler fragments, we have to put it all together, The final equation should look like the one below!
![tan(\pi + Theta) = \frac{0 + tanTheta}{1 - 0} = tanTheta](https://tex.z-dn.net/?f=tan%28%5Cpi%20%2B%20Theta%29%20%3D%20%5Cfrac%7B0%20%2B%20tanTheta%7D%7B1%20-%200%7D%20%3D%20tanTheta)
With that information, we have solved the problem, your final answer is tanɵ
What have we learned?
<h3>We learned some knowledge on what simplifying expressions with complex mathematical terms looks like.</h3>