Question

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

• A. $\frac{5}{14}$
• B. $\frac{3}{14}$
• C. $\frac{1}{14}$
• D. $0$

Answer 1

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

$5\tan \theta =4$

$\Rightarrow \tan \theta =\frac{4}{5}$

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

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

$=\frac{1}{\frac{14}{5}}$

$=\frac{5}{14}$

Hence, the answer is $\frac{5}{14}.$