Opposites Theorem

Proof
From Basic Properties of Sine Function, we have:
 * $\sin \left({- \theta}\right) = - \sin \theta$

From Basic Properties of Cosine Function, we have:
 * $\cos \left({- \theta}\right) = \cos \theta$

Then we have:

Comment
The concept of bagging up these straightforward identities into one, and calling it the Opposites Theorem, seems to be a modern innovation.