<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["fr", "en"].<end_of_turn>
<start_of_turn>user
Expliquez le théorème du cosinus.<end_of_turn>
<start_of_turn>model
The theorem or rule or law of cosines is a generalization of the Pythagorean theorem for non-right triangles. This says that the square of the length of any one side is equal to the sum of the squares of the lengths of the other two sides, minus twice the product of those two sides multiplied by the cosine of the angle opposite the first mentioned side.

More precisely, if we have a triangle whose sides are a,b,c and the interior angles opposite to these sides are alpha, beta and gamma respectively, then:

c^2 = a^2 + b^2 - 2*a*b*cos(gamma)

We can see that the Pythagorean theorem is a particular case of this theorem, since when gamma=90 degrees, we obtain cos(gamma) = 0, and therefore c^2 = a^2 + b^2.<end_of_turn><eos>