Question

If $5\tan \theta =4$, find the value of $\frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$

• A. 2
• B. $\frac{3}{2}$
• C. $\frac{1}{6}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{1}{6}$

Given that $5\tan \theta =4\therefore \tan \theta =4/5$
$\therefore \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }=\frac{\frac{5\sin \theta }{\cos \theta }-3}{\frac{5\sin \theta }{\cos \theta }+2}$
[Dividing both the numerator and denominator by $\cos \theta$]
$=\frac{5\tan \theta -3}{5\tan \theta +2}$
$=\frac{5\times \frac{4}{5}-3}{5\times \frac{4}{5}+2}[\because \tan \theta =\frac{4}{5}]$
$=\frac{4-3}{4+2}=\frac{1}{6}$