A) \[7\]
B) \[-\,\,7\]
C) \[\frac{1}{7}\]
D) \[\frac{2}{7}\]
Correct Answer: A
Solution :
\[16\cot \theta =12\] \[\Rightarrow \]\[\cot \theta =\frac{12}{16}=\frac{3}{4}\] \[\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{\frac{\sin \theta }{\sin \theta }+\frac{\cos \theta }{\sin \theta }}{\frac{\sin \theta }{\sin \theta }-\frac{\cos \theta }{\sin \theta }}\] \[=\frac{1+\cot \theta }{1-\cot \theta }=\frac{1+\frac{3}{4}}{1-\frac{3}{4}}=\frac{7/4}{1/4}=7\]
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