Example 2. $\sin 2 \alpha=-\frac{24}{25}$ and $\frac{3}{4} \pi<\alpha<\pi$, then the value of tg $\boldsymbol{\alpha}$ is
(A) $\frac{4}{3}$ or $\frac{3}{4}$,
(B) $-\frac{4}{3}$ or $-\frac{3}{4}$,
(C) $-\frac{4}{3}$,
(D) $-\frac{3}{4}$.
Using the universal formula to verify, $-\frac{4}{3}$ and $-\frac{3}{4}$ are both possible, which would lead to mistakenly choosing $B$. However, an implicit condition is overlooked: due to the monotonicity of $\tan \alpha$, when $\frac{3}{4} \pi < \alpha < \pi$, $-1 < \tan \alpha < 0$. Therefore, $-\frac{4}{3}$ cannot be selected, and the correct choice is (D).