Final answer:
The question asks to show that two equations represent the same metric through a coordinate transformation from Cartesian to spherical. However, without the explicit forms of the equations, the verification cannot be performed in this response. Correct option is (C) verify.
Step-by-step explanation:
The student's question involves demonstrating that two equations (presumably equations 3.29 and 3.30, whose content is not mentioned) represent the same metric by making the substitutions x=rsinθcosφ, y=rsinθsinφ, and z=rcosθ. This task relates to spherical coordinates and their relationship to Cartesian coordinates, and it may be part of a larger discussion on coordinate transformations or the geometry of space in physics, particularly in the study of vector fields or general relativity.
Without the explicit forms of equations 3.29 and 3.30, the verification process cannot be executed. Typically, such a verification would involve substituting the expressions for x, y, and z into the two given equations and showing that one can be transformed into the other, thereby proving that they are indeed expressions of the same metric.