It's been about 20 years since I did any trig, but my daughter (no pics) is now in trig. We ran into a problem we couldn't solve last night. And I have vague memories of doing this exact problem in high school.
The odd/even identities state that tan(-x) = -tan(x). The same is true for cos, sin, cot, etc.
Tan(x) = sin(x)/cos(x). So, tan(-x) = sin(-x)/cos(-x). But then you bring out the negative signs, and you get -sin(x)/-cos(x). And since this is a negative over a negative, you get sin(x)/cos(x), which = tan(x).
I know I'm making an incorrect assumption somewhere. I even ran sin(-x)/cos(-x) and -sin(x)/-cos(x) through Wolfram Alpha, and got -tan(x) and tan(x), respectively. And tan(-x) doesn't equal tan(x) and -tan(x) doesn't equal tan(x).
Isn't this a classic trig problem?