A) \[\frac{2}{5}\]
B) \[\frac{1}{7}\]
C) \[\frac{3}{4}\]
D) \[\frac{5}{6}\]
Correct Answer: B
Solution :
\[4\cot \theta =3\]\[\Rightarrow \]\[\cot \theta =\frac{3}{4}\] \[\left( \frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta 0} \right)=\left( \frac{1-\frac{\cos \theta }{\sin \theta }}{1+\frac{\cos \theta }{\sin \theta }} \right)=\left( \frac{1-\cot \theta }{1+\cot \theta } \right)\] \[=\frac{\left( 1-\frac{3}{4} \right)}{\left( 1+\frac{3}{4} \right)}=\frac{\frac{1}{4}}{\frac{7}{4}}=\frac{1}{7}\]
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