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