Undergraduate / "Ok class. You may start."; Stanford Intellectual Vitality [2]

"Ok class. You may start."

I quickly turned the paper over and there was only 1 problem:

"Show that (Tan(x+y)=x) = -(x^2)/(x^(2)-1)"

As it was a test over derivatives, I knew I'd have to apply some sort of derivative rule to solve this beast. As I couldn't isolate y, I decided that implicit differentiation would be the best approach. But when I reached what seemed like a dead end in the form of -sin(x+y), I almost gave up. I couldn't simplify any further. 5 min left. I started to worry. Then it hit me.

"What if I draw a triangle?"

Since tangent is opposite over adjacent, the opposite side must equal x and the adjacent is 1. The hypotenuse would then be √(x^2 + 1). Sin(x+y) would then equal x/√(x^2 + 1). Squaring the top and bottom would result in x^(2)/(x^2 + 1). Then add a negative sign because I had negative sin, and there lay my answer. I quickly wrote down the answer and submitted my paper.

The A was a nice gift, but my true reward was the application of other disciplines of mathematics to help reach what seemed like an improbable solution. Never would I have thought that a quick lesson in Pre-Calculus would save my butt and propel me to the top of my class. Our teacher said to think outside the box; how about outside the triangle?

Feedback and thought are very helpful, as English really isn't my strongest subject! Please don't be afraid to be critical as well!