Question

If $3\cot \theta =4$ then $\frac{5\sin \theta +3\cos \theta }{5\sin \theta -3\cos \theta }=$_____

• A. $\frac{1}{3}$
• B. $3$
• C. $\frac{1}{9}$
• D. $9$

Answer 1

The correct option is D $9$

We know that, $cot\theta =\frac{sin\theta }{cos\theta }$

Given:

$\cot \theta =\frac{4}{3}$

Thus, $\frac{5\sin \theta +3\cos \theta }{5\sin \theta -3\cos \theta }=\frac{5+3\cot \theta }{5-3\cot \theta }$

($\because$ dividing the numerator and denominator by $\sin \theta$)

$=\frac{5+3\times \frac{4}{3}}{5-3\times \frac{4}{3}}=9$.

Hence option (D) is coorect