Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 173: 59

$x = \frac{5\pi}{4} + \pi~n$, where $n$ is any integer

The function $y = -2-cot(x-\frac{\pi}{4})$ is undefined when $x = \frac{5\pi}{4}$ We can find the general form of the equation of the asymptotes: $x = \frac{5\pi}{4} + \pi~n$, where $n$ is any integer