Question : If $6 \cot \theta=5$, then find the value of $\frac{(6 \cos \theta+\sin \theta)}{(6 \cos\theta-4 \sin\theta)}$
Option 1: 5
Option 2: 1
Option 3: 6
Option 4: 0
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Correct Answer: 6
Solution :
$6 \cot \theta = 5$
⇒ $\cot \theta = \frac{5}{6}$
Now, $\frac{(6 \cos \theta+\sin \theta)}{(6 \cos \theta-4\sin \theta)}$
Dividing numerator and denominator by $\sin \theta$ in the above expression
⇒ $\frac{(6 \cos \theta+\sin \theta)}{(6 \cos \theta-4\sin \theta)}=\frac{(6\cot \theta + 1)}{(6\cot \theta-4)}$
$=\frac{6 \times \frac{5}{6} + 1}{6\times \frac{5}{6}-4}$
$= \frac{5 + 1}{5-4}$
$=6$
Hence, the correct answer is 6.
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