Question

If $5\tan \theta =4$ , then the value of $\frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$ will be equal to:

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{4}{5}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

$\frac{1}{6}$

$5\tan \theta =4$

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

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

$=\frac{4-3}{4+2}=\frac{1}{6}$