Question

If $3\cot \theta =5$, then $\frac{5\sin \theta -3\cos \theta }{5\sin \theta +3\sin \theta }$= _____.

• A. $\frac{5}{3}$
• B. $\frac{3}{5}$
• C. $0$
• D. $\frac{4}{5}$

Answer 1

The correct option is C $0$

Given $3\cot \theta =5$

$\frac{5\sin \theta -3\cos \theta }{5\sin \theta +3\sin \theta }=\frac{5\sin \theta -3\cos \theta }{8\sin \theta }$

$=\frac{5}{8}-\frac{3\cot \theta }{8}$

$=\frac{5}{8}-\frac{5}{8}$ $(\because 3\cot \theta =5)$

$=0$