Trigonometric Identities Question 18
Question: The value of $\frac{\tan x}{\tan 3 x}$ whenever defined never lie between
[Kurukshetra CEE 1998; IIT 1992]
Options:
A) $ \frac{1}{3} $ and 3
B) $ \frac{1}{4} $ and 4
C) $ \frac{1}{5} $ and 5
D) 5 and 6
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y=\frac{\tan x}{\tan 3x}=\frac{\tan x}{\frac{3\tan x-{{\tan }^{3}}x}{1-3{{\tan }^{2}}x}} $ $ y=\frac{1-3{{\tan }^{2}}x}{3-{{\tan }^{2}}x}=\frac{\frac{1}{3}-{{\tan }^{2}}x}{1-\frac{1}{3}.{{\tan }^{2}}x} $ Hence, y should never lie between $ \frac{1}{3} $ and 3 whenever defined.
BETA
