A) \[\frac{1}{7}\]
B) \[\frac{2}{7}\]
C) \[\frac{5}{7}\]
D) \[\frac{2}{5}\]
Correct Answer: A
Solution :
\[5\tan \theta =4\Rightarrow \tan \theta \frac{4}{5}\] \[\therefore \]\[\frac{5\sin \theta -3\cos \theta }{5\sin \theta +3\cos \theta }=\frac{\frac{5\sin \theta -3\cos \theta }{\cos \theta }}{\frac{5\sin \theta +3\cos \theta }{\cos \theta }}\] \[=\frac{5\tan \theta -3}{5\tan \theta +3}=\frac{5\times \frac{4}{5}-3}{5\times \frac{4}{5}+3}=\frac{4-3}{4+3}=\frac{1}{7}\]
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