Question

If $\theta$ lies in the first quadrant and $5\tan \theta =4$, find $\frac{5\sin \theta -3\cos \theta }{\sin \theta +2\cos \theta }$

• A. $\frac{2}{3}$
• B. $\frac{3}{14}$
• C. $\frac{5}{14}$
• D. $0$

Answer 1

The correct option is C $\frac{5}{14}$

$\frac{5\sin \theta -3\cos \theta }{\sin \theta +2\cos \theta }=\frac{5\tan \theta -3}{\tan \theta +2}=\frac{4-3}{(\frac{4}{5}+2)}$

$=\frac{5}{14}$.