can somone help me?? to prove tan3xtan2xtanx= tan3x-tan2x-tanx

Question

anonymous · Answer

tan x + tan 2x + tan 3x - tan x tan 2x tan 3x = 0 

=> tan x + tan 2x + tan 3x ( 1 - tan x tan 2x ) = 0 

=> tan x + tan 2x = - tan 3x ( 1 - tan x tan 2x ) 

=> ( tan x + tan 2x )/ ( 1 - tan x tan 2x ) = - tan 3x

=> tan 3x = - tan 3x

=> 2 tan 3x = 0 

=> tan 3x = 0 

=> 3x = 2kpi where k = 0, 1,2,3,4,5,..............

=> x = 2 k pi/3 where k = 0 , 1, 2 ,3 , 4 , 5 , 6..............

anonymous · Answer

3x=2x+x
applying tan b/s
tan3x=tan(2x+x)
tan3x=tan2x+tanx\1-tan2xtanx
tan3x(1-tan2xtanx)=tan2x+tanx
tan3x-tan3xtan2xtanx=tan2x+tanx
tan3x-tan2x-tanx=tan3xtan2xtanx

anonymous · Answer

tysm!!!!!!