Step-by-step Solution:

Given that \( \sin x = \sin y \) and \( \cos x = \cos y \), we need to determine the value of \( x - y \). \[\] Using the cosine addition formula: \[ \cos(x - y) = \cos x \cdot \cos y + \sin x \cdot \sin y \] Substituting \( \sin x = \sin y \) and \( \cos x = \cos y \) into the equation: \[ \cos(x - y) = \cos x \cdot \cos x + \sin x \cdot \sin x \] Simplifying the right-hand side: \[ \cos(x - y) = \cos^2 x + \sin^2 x \] Using the Pythagorean identity \( \cos^2 x + \sin^2 x = 1 \), we get: \[ \cos(x - y) = 1 \] From \( \cos(x - y) = 1 \), it follows that: \[ x - y = 2n\pi \quad \text{for some integer} \, n \] Thus, the value of \( x - y \) is: \[ x - y = 2n\pi \] where \( n \) is any integer.