MCQ
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$\frac{1}{9}$
- ✓$9$
✓
Answer
Correct option: D.
$9$
Given, $3\cot\theta=4$
Now, $\frac{(5\sin\theta+3\cos\theta)}{(5\sin\theta-3\cos\theta)} $
$=\frac{\frac{5\sin\theta}{\sin\theta}+\frac{3\cos\theta}{\sin\theta}}{\frac{5\sin\theta}{\sin\theta}-\frac{3\cos\theta}{\sin\theta}}$
$=\frac{5+3\cot\theta}{5-3\cot\theta}$
$=\frac{5+4}{5-4}$
$=\frac{9}{1}$
$=9$
Now, $\frac{(5\sin\theta+3\cos\theta)}{(5\sin\theta-3\cos\theta)} $
$=\frac{\frac{5\sin\theta}{\sin\theta}+\frac{3\cos\theta}{\sin\theta}}{\frac{5\sin\theta}{\sin\theta}-\frac{3\cos\theta}{\sin\theta}}$
$=\frac{5+3\cot\theta}{5-3\cot\theta}$
$=\frac{5+4}{5-4}$
$=\frac{9}{1}$
$=9$
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