Final answer:
The correct form of the law of cosines is A) a² = b² + c² + 2bc cos A, with the understanding that there should be a minus sign before the 2bc cos A part to match the conventional formula c² = a² + b² - 2ab cos y.
Step-by-step explanation:
The correct form of the law of cosines is given by the equation c² = a² + b² - 2ab cos y. This formula enables us to find the length of one side of any triangle when we know the lengths of the other two sides as well as the measure of the included angle. It is a generalization of the Pythagorean theorem, which applies only to right triangles, whereas the law of cosines can be applied to any triangle.
Looking at the options given in the question, the correct form of the law of cosines is A) a² = b² + c² + 2bc cos A, although it should be correctly written as a² = b² + c² - 2bc cos A to match the formula we have established.