1. Given $7 \sin \alpha + 24 \cos \alpha = 25$. Then $\tan \alpha =$ ().
(A) $\frac{3}{4}$
(B) $\frac{4}{3}$
(C) $\frac{24}{7}$
(D) $\frac{7}{24}$
- 1.D.

From $25^{2}=(7 \sin \alpha+24 \cos \alpha)^{2}+$ $(7 \cos \alpha-24 \sin \alpha)^{2}$,

we have $7 \cos \alpha-24 \sin \alpha=0$. Therefore, $\tan \alpha=\frac{7}{24}$.