Question

Show that
tan 3 x tan 2 x tan x = tan 3x - tan 2 x – tan x​

Answer 1

Step-by-step explanation:

we are using here the given formula

$\tan(a + b) = \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) }$

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

on cross multiplication,

$\tan(3x) - \tan(3x) \tan(2x) \tan(x) = \tan(2x) + \tan(x) \\ \tan(3x) - \tan(2x) - \tan(x) = \tan(3x) \tan(2x) \tan(x)$

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