Question

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

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

Answer 1

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

Divide the numerator and denomenator by $\cos \theta$
$\frac{\frac{5\sin \theta -3\cos \theta }{\cos \theta }}{\frac{5\sin \theta +2\cos \theta }{\cos \theta }}\Rightarrow \frac{\frac{5\sin \theta }{3\cos \theta }-\frac{3\cos \theta }{\cos \theta }}{\frac{5\sin \theta }{\cos \theta }+\frac{2\cos \theta }{\cos \theta }}\Rightarrow \frac{5\tan \theta -3}{5\tan \theta +2}$
Substituting the value of $5\tan \theta$, we get
$\Rightarrow$ $\frac{4-3}{4+2}=\frac{1}{6}$