A) \[\frac{1}{7}\]
B) \[\frac{2}{7}\]
C) \[\frac{5}{7}\]
D) \[\frac{2}{5}\]
Correct Answer: A
Solution :
| [a] \[\frac{5\sin \theta -3\cos \theta }{5\sin \theta +3\cos \theta }=\frac{\cos \theta \left( \frac{5\sin \theta }{\cos \theta }-3 \right)}{\cos \theta \left( 5\frac{\sin \theta }{\cos \theta }+3 \right)}\] \[=\frac{5\sin \theta -3}{5\tan \theta +3}=\frac{5\cdot \frac{4}{5}-3}{5\cdot \frac{4}{5}+3}\] \[(\therefore 5tan\theta =4)\] \[=\frac{1}{7}\] |
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