Tính a + b.

Trả lời: 43

Ta có \(A = \frac{{4\sin \alpha  + 3\cos \alpha }}{{5\sin \alpha  + 2\cos \alpha }}\)\( = \frac{{4\frac{{\sin \alpha }}{{\cos \alpha }} + 3}}{{5\frac{{\sin \alpha }}{{\cos \alpha }} + 2}}\)\( = \frac{{4\tan \alpha  + 3}}{{5\tan \alpha  + 2}}\)\( = \frac{{4.\frac{2}{5} + 3}}{{5.\frac{2}{5} + 2}} = \frac{{23}}{{20}}\).

Suy ra \(a = 23;b = 20\). Do đó \(a + b = 43\).