In order to understand the proof below, you must have a prior knowledge about circular functions. The proof also uses symmetry which is I think quite basic for high schools students. The basic idea is that the point $latex (x,y)$ is symmetric with the point $latex (x,-y)$ with respect to the $latex x$ axis.

The angles $latex \theta$ and $latex -\theta$ are rotations with the positive x-axis as the initial side. The angle $latex \theta$ is a counterclockwise rotation and the angle $latex – \theta$ is a clockwise rotation as shown by the arrows in the diagram below.

**Theorem**

In this short post, we are going to prove the following trigonometric identities: Continue reading