Trigonometric Identities Question 61

Question: $ \tan 3A-\tan 2A-\tan A= $

[MNR 1982; Pb. CET 1991]

Options:

A) $ \tan 3A\tan 2A\tan A $

B) $ -\tan 3A\tan 2A\tan A $

C) $ \tan A\tan 2A-\tan 2A\tan 3A-\tan 3A\tan A $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

Since $ \tan 3A=\frac{\tan A+\tan 2A}{1-\tan A\tan 2A} $
$ \Rightarrow \tan 3A-\tan 2A-\tan A=\tan 3A,\tan 2A\tan A $ .