Question

prove that. tan 3x ×tan 2x ×tan x =tan3x - tan 2x - tan x

Answer 1

hello... ☺


let
3x = 2x➕ x

take tan on both side

tan3x = tan (2x➕x)

tan3x = (tan2x➕tanx)➗1➖tan2x tanx

(1➖tan2x tanx)tan3x = tan2x➕tanx

tan3x ➖tanx tan2x tan3x = tan2x➖tanx

tanx tan2x tan3x = tan3x➖tan2x➖tanx

hence proved!!!


thank you ☺

Answer 2

We know that,

$3x = 2x + x$

Taking tan on both sides

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

By using identity of tan. i.e.,

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

We get

$\tan(3x) = \frac{ \tan(2x) + \tan(x) }{1 - \tan(2x) \tan(x) } \\ \\ on \: cross \: multiplication \\ \\ \tan(3x) - \tan(3x) \tan(2x) \tan(x) \\= \tan(2x) + \tan(x)$

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

⭐HOPE IT MAY HELP YOU⭐