Chapter 8, Problem 75E

Using $J^2=L^2+S^2+2\text{L}\cdot \text{S}$ to eliminate $\text{L}\cdot \text{S}$ , as well as $L=\sqrt{\mathcal{l}\left(\mathcal{l}+1\right)}\hslash$ , $S=\sqrt{s\left(s+1\right)}\hslash$ , and $J=\sqrt{j\left(j+1\right)}\hslash$ , obtain equation (8−32) from the equation that precedes it.