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Question
tan 3A − tan 2A − tan A =
Options
tan 3 A tan 2 A tan A
−tan 3 A tan 2 A tan A
tan A tan 2 A − tan 2 A tan 3 A − tan 3 A tan A
None of these
Solution
\[3A = 2A + A\]
\[ \Rightarrow \tan 3 A = \tan(2A + A)\]
\[ = \frac{\tan2A + \tan A}{1 - \tan2A\tan A}\]
\[ \Rightarrow \tan 3A - \tan3A \tan2A \tan A = \tan 2A + \tan A\]
\[ \Rightarrow \tan 3A - \tan 2A - \tan A = \tan3A \tan2A \tan A\]
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