The tan(-x) is the same thing as -tan(x). The tangent function is also the same thing as sin(x)/cos(x), right? So let's rewrite that tan in terms of sin and cos:
![[cos(x)][tan(-x)]](https://tex.z-dn.net/?f=%5Bcos%28x%29%5D%5Btan%28-x%29%5D)
is the same as ![[cos(x)][ -\frac{sin(x)}{cos(x)}]](https://tex.z-dn.net/?f=%5Bcos%28x%29%5D%5B%20-%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D%5D%20)
We can now cancel out the cos(x), which leaves us only with -sin(x) remaining. So your answer is A.
We can now cancel out the cos(x), which leaves us only with -sin(x) remaining. So your answer is A.