# Is this maths equation leading me through the first or second door?

I needed to speak to my professor who has gone into hiding.

I followed her directions, leading me underneath the university until I got to corridor with two doors, labeled with the Roman Numerals: I and II.

The next step in the directions looked as follows:

$$? = \frac{\frac{2ab}{a^{2}+b^2-c^2}}{D}$$

How is this supposed to help? Which door should I take?

• what i'm concerned about is why your professor felt the need to go into hiding, and how did she even know that there were these secret system of tunnels under the university? it almost sounds like she was actually a villain all this time, who is now trying to lure her brightest students into her trap!! Jul 1, 2022 at 13:53

You should enter door

II as it's the secConD

Simplifying the formula using

the cosine rule $${a^{2}+b^2-c^2} = 2ab\cos C$$ gives

$$\frac{1}{D\cos C}$$ which is

$$\frac{\sec C}{D}$$ or as a rebus secConD

• beat me to it by a matter of a moment.. Jun 30, 2022 at 17:41
• @Konchog - maybe by 1s. It's a very enjoyable question, and the first time I've applied this rule outside of a school setting.
– Tom
Jun 30, 2022 at 17:46
• @Tom that's correct and I'm glad you enjoyed it! Jun 30, 2022 at 18:08