Question

If $5\tan \theta =4$, then $\frac{5\sin \theta -3\cos \theta }{\sin \theta +2\cos \theta }$=

• A. $\frac{5}{9}$
• B. $\frac{14}{5}$
• C. $\frac{9}{5}$
• D. $\frac{5}{14}$

Answer 1

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

Given $5+\tan \theta =4$

$\therefore \tan \theta =4/5$

We have,$\frac{5\sin \theta -3\cos \theta }{\sin \theta +2\cos \theta }$

Devide by $\cos \theta$ in Numerator & Denominator

$=\frac{\frac{5\sin \theta }{\cos \theta }-3}{\frac{\sin \theta }{\cos \theta }+2}$

$=\frac{5\tan \theta -3}{\tan \theta +2}$

$=\frac{4-3}{4/5+2}$

$=\frac{1}{\frac{4+10}{5}}$

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