If 5sinθ - 4cosθ = 0, 0° < θ < 90°, then the value of $$\frac{{5\sin \theta - 2\cos \theta }}{{5\sin \theta + 3\cos \theta }}$$   is:

Solution (By Examveda Team)

$$\eqalign{ & 5\sin \theta - 4\cos \theta = 0 \cr & 5\sin \theta = 4\cos \theta \cr & \frac{{\sin \theta }}{{\cos \theta }} = \frac{4}{5} \cr & \tan \theta = \frac{4}{5} \cr & \frac{{5\sin \theta - 2\cos \theta }}{{5\sin \theta + 3\cos \theta }} \cr & = \frac{{5\tan \theta - 2}}{{5\tan \theta + 3}} \cr & = \frac{{5 \times \frac{4}{5} - 2}}{{5 \times \frac{4}{5} + 2}} \cr & = \frac{2}{7} \cr} $$