tan 3 x - tan 2 x - tan x is equal to

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Solution

Q.
$\tan 3 x - \tan 2 x - \tan x$ is equal to

1 $\tan x \tan 2 x \tan 3 x$

2 $- \tan x \tan 2 x \tan 3 x$

3 $\tan x \tan 2 x - \tan x \tan 3 x - \tan 2 x \tan 3 x$

4 none of these

Ans.
(1)

$\tan 3 x = \tan (2 x + x) = \frac{\tan 2 x + \tan x}{1 - \tan 2 x \tan x}$

$∴$ $\tan 3 x - \tan 3 x \tan 2 x \tan x = \tan 2 x + \tan x$

$∴$ $\tan 3 x - \tan 2 x - \tan x = \tan 3 x \tan 2 x \tan x$

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