A) \[\ge 0\] only when \[\theta \ge 0\]
B) \[\le 0\] for all real \[\theta \]
C) \[\ge 0\] for all real \[\theta \]
D) \[\le 0\]only when \[\theta \le 0\]
Correct Answer: C
Solution :
Here, \[f(\theta )=\sin \theta (\sin \theta +\sin 3\theta )\] \[=\sin \theta (\sin \theta +3\sin \theta -4{{\sin }^{3}}\theta )=4{{\sin }^{2}}\theta (1-{{\sin }^{2}}\theta )\] \[=4{{\sin }^{2}}\theta {{\cos }^{2}}\theta ={{(\sin 2\theta )}^{2}}\] \\[f(\theta )\ge 0\] for all real \[\theta \].
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