A) \[\frac{{{\sin }^{2}}\theta }{\cos \theta }\]
B) \[\tan \theta \]
C) \[\frac{{{\cos }^{2}}\theta }{\sin \theta }\]
D) \[\cot \theta \]
Correct Answer: B
Solution :
\[\frac{\sin \theta -2{{\sin }^{3}}\theta }{2{{\cos }^{3}}\theta -\cos \theta }=\frac{\sin \theta }{\cos \theta }\,\left[ \frac{1-2{{\sin }^{2}}\theta }{2{{\cos }^{2}}\theta -1} \right]\] \[=\frac{\sin \theta }{\cos \theta }\left[ \frac{1-2(1-{{\cos }^{2}}\theta )}{2{{\cos }^{2}}\theta -1} \right]\] \[=\frac{\sin \theta }{\cos \theta }\left[ \frac{2{{\cos }^{2}}\theta -1}{2{{\cos }^{2}}\theta -1} \right]=\tan \theta \]
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