Trigonometric Identities Question 316
Question: The value of $ \tan A+\tan (60{}^\circ +A)-\tan (60{}^\circ -A) $ is
Options:
A) $ \tan 3A $
B) $ 2tan 3A $
C) $ 3tan3A $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
The given expression $ =\tan A+[ \frac{\sqrt{3}+\tan A}{1-\sqrt{3}\tan A} ]-[ \frac{\sqrt{3}-\tan A}{1+\sqrt{3}\tan A} ] $ $ =\tan A+[ \frac{8\tan A}{1-3{{\tan }^{2}}A} ]=\frac{9\tan A-3{{\tan }^{3}}3}{1-3{{\tan }^{2}}A} $ $ =3.\frac{(3\tan A-{{\tan }^{3}}A)}{1-3{{\tan }^{2}}A}=3\tan 3A $
BETA
