Question # 33. For O

# 33. For O

Solution ( begin{aligned} & tan x+tan 2 x+tan 3 x=0 Rightarrow &left(frac{tan x+tan 2 x}{1-tan x cdot tan 2 x}right)(1-tan x cdot tan 2 x)+tan 3 x=0 end{aligned} )
( Rightarrow tan 3 x(1-tan x cdot tan 2 x)+tan 3 x=0 quadleft(therefore tan (x+y)=frac{tan x+tan y}{1-tan x+tan y}right) )
( Rightarrow tan 3 x[2-tan x cdot tan 2 x]=0 )
So, either tan ( 3 x=0 ) or ( 2-tan x cdot tan 2 x=0 )

Solution