Trigonometric Identities Question 6
Question: If $ \tan x+\tan ( \frac{\pi }{3}+x )+\tan ( \frac{2\pi }{3}+x )=3, $ then
Options:
A) $ \tan x=1 $
B) $ \tan 2x=1 $
C) $ \tan 3x=1 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \tan x+\tan ,( \frac{\pi }{3}+x )+\tan ,( \frac{2\pi }{3}+x ) $ $ =\tan x+\frac{\tan x+\sqrt{3}}{1-\sqrt{3},\tan x}+\frac{\tan x-\sqrt{3}}{1+\sqrt{3},\tan x} $ $ =\tan x+\frac{8\tan x}{1-3{{\tan }^{2}}x}=\frac{3,(3\tan x-{{\tan }^{3}}x)}{1-3{{\tan }^{2}}x}=3\tan 3x $ Therefore, the given equation is $ 3\tan 3x=3 $
Þ $ \tan 3x=1. $
BETA
