Question : What is the value of the given expression if $3\cot A=\frac{7}{3}$?
$\frac{3 \cos A+2 \sin A}{3 \cos A-2 \sin A}$
Option 1: $\frac{2}{3}$
Option 2: $\frac{1}{3}$
Option 3: $13$
Option 4: $1$
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Correct Answer: $13$
Solution :
Given: $3\cot A=\frac{7}{3}$
To find: $\frac{3 \cos A+2 \sin A}{3 \cos A-2 \sin A}$
Dividing numerator and denominator by $\sin A$, we get:
$= \frac{\frac{3 \cos A}{\sin A}+\frac{2 \sin A}{\sin A}}{\frac{3 \cos A}{\sin A}-\frac{2 \sin A}{\sin A}}$
$= \frac{3\cot A+2}{3\cot A-2}$
Putting $3\cot A=\frac{7}{3}$
$= \frac{\frac{7}{3}+2}{\frac{7}{3}-2}$
$= \frac{13}{1}= 13$
Hence, the correct answer is $13$.
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