1. Given $0<x<\frac{\pi}{2}, \sin x-\cos x=\frac{\pi}{4}$, if $\tan x+\frac{1}{\tan x}$ can be expressed in the form $\frac{a}{b-\pi^{c}}$, where $a$, $b$, and $c$ are positive integers, then $a+b+c=(\quad)$.
(A) 8
(B) 32
(C) 48
(D) 50