Question

Найдите 4sina-7cosa/sina-4cosa если tga=5​

Answer 1

$\displaystyle tg \alpha=\frac{\sin \alpha}{\cos \alpha} =5 \Rightarrow \sin \alpha=5\cos\alpha\\\frac{4 \sin \alpha - 7\cos \alpha}{\sin \alpha - 4\cos \alpha} =\frac{4\cdot 5\cos\alpha - 7\cos \alpha}{5\cos\alpha - 4\cos \alpha} =\frac{13 \cos \alpha }{\cos \alpha} = 13\\\\OTBET: \; 13$