The value of x ,3x whenever defined never lie between - Vidyadip

MCQ

The value of $\frac{{\tan x}}{{\tan \,3x}}$ whenever defined never lie between

✓
$1/3$ and $3$
B
$1/4 $ and $4$
C
$1/5$ and $5$
D
$5$ and $6$

✓

Answer

Correct option: A.

$1/3$ and $3$

a
(a) 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.

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