MathNet 2007-part-01 — 187 problems (EN–VI) Question 131

Let $f(x) = 3\sin x + 2\cos x + 1$. If real numbers $a, b, c$ are such that $af(x) + bf(x-c) = 1$ holds for any $x \in \mathbb{R}$, then $\frac{b\cos c}{a}$ equals ( ).