Question

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

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

Answer 1

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

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

$\therefore \frac{5\sin \theta -3\cos \theta }{\sin \theta +2\cos \theta }=\frac{5\tan \theta -3}{\tan \theta +2}=\frac{5\times \frac{4}{5}-3}{\frac{4}{5}+2}=\frac{5}{14}$