Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 489: 84

$-\frac{1}{7}$

Step 1. Letting $cos^{-1}\frac{3}{5}=t$, we have $cos(t)=\frac{3}{5}$ and $tan(t)=\frac{4}{3}$ Step 2. We have $tan(\frac{\pi}{4}-t)=\frac{tan(\frac{\pi}{4})-tan(t)}{1+tan(\frac{\pi}{4})tan(t)}=\frac{1-4/3}{1+4/3}=-\frac{1}{7}$