Question : If $8 \cot \theta=6$, then the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}$ is:
Option 1: 12
Option 2: 7
Option 3: 2
Option 4: 5
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Correct Answer: 7
Solution :
$8 \cot \theta = 6$
$\therefore \cot \theta = \frac{6}{8}$
Now, $\frac{(\sin \theta+\cos \theta)}{(\sin \theta-\cos \theta)}$
Dividing numerator and denominator by $\sin \theta$
$=\frac{(1+\cot \theta )}{(1-\cot \theta)}$
$=\frac{1+ \frac{6}{8}}{1- \frac{6}{8}}$
$=\frac{\frac{14}{8}}{\frac{2}{8}}$
$=\frac{14}{2}$
$=7$
Hence, the correct answer is 7.
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