This is the cosine theorem, which is a key knowledge point. The proof is as follows.

Draw a picture to know the details, at △ABC.

From the addition and subtraction of vectors, we can know that vector BC= vector AC- vector AB.

Square both sides at the same time to get BC square =AC square +AB square -2AB AC COSA.

So we get a square =b square +c square -2bccosA,

You get the plus sign because the cosA you calculated is the complementary angle of the original COSA, so COSA should be the minus sign in front.