A) \[4\sin \theta (1-2{{\sin }^{2}}\theta )\sqrt{1-{{\sin }^{2}}\theta }\]
B) \[2\sin \theta \cos \theta {{\sin }^{2}}\theta \]
C) \[4\sin \theta -6{{\sin }^{3}}\theta \]
D) None of these
Correct Answer: A
Solution :
\[\sin 4\theta =2\sin 2\theta \cos 2\theta \] \[=2.2\sin \theta \cos \theta (1-2{{\sin }^{2}}\theta )\] \[=4\sin \theta (1-2{{\sin }^{2}}\theta )\sqrt{1-{{\sin }^{2}}\theta }\]
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