A couple of demonstrations of the sine and cosine of the addition of two angles

This is a problem that was send for us in MA1121, and although I haven't found my own way I've got two ways to demonstrate it that I found this early morning when I was studying for my quiz of today:

By similitude of triangles

Rotating the axes

Haciendo uso del hecho de que a cada punto del plano le corresponde un vector y de que los vectores se suman según la regla del paralelogramo, vamos a demostrar las fórmulas para el seno y el coseno de la suma de dos ángulos en función de los senos y cosenos de cada uno de ellos. Concretamente vamos a demostrar las siguientes igualdades: Rest of the explaination at http://gaussianos.com/el-seno-y-el-coseno-de-la-suma-de-angulos/

Perhaps you were doing this, and now you feel spoiled, if that's the case then I let you another problem from Gaussianos.com that is really fod for thought:

Demonstrate that every triangle ABC that verifies that

is right angled.