Final answer:
The student seeks the first error in a mathematical proof for the equation z² = z² y² - 2yz cos(x), but without the actual proof provided, it is impossible to identify any errors or to evaluate the validity of the equation.
Step-by-step explanation:
The student is attempting to prove the equation z² = z² y² - 2yz cos(x), and we are to determine where the first error is made in the proof. However, based on the information provided, there is no explicit proof to analyze for errors. The relationship resembles a form of the Law of Cosines, which relates the lengths of sides of a triangle with the cosine of one of its angles but requires the context of a triangle and accurate representation of the sides and angles involved.
Due to insufficient information to identify a starting point for the proof or the first error in that proof, it is impossible to provide a step-by-step correction or validation of it. We need the complete proof attempted by the student to properly identify where the error occurs and correct it accordingly.