Solve the following equations: (i) tan x + tan 2x + tan 3x = 0 (ii) tan x + tan 2x = tan 3x

The general solution of any trigonometric equation is given as:

   

or

   

where n ∈ Z.

   

   

where n ∈ Z.

   

or,

   

where n ∈ Z.

   

Or,

   

   

By using the formula,

   

So,

   

   

   

Or,

   

Then,

   

   

Or,

   

   

   

   

Or,

   

   

Or,

   

or

   

   

or

   

   

or

   

   

or

   

   

or

   

   

   

or

   

∴ the general solution is

   

where

   

   

Or,

   

   

or,

   

By using the formula,

   

So,

   

   

Or,

   

Then,

   

or

   

Or,

   

Or,

   

or,

   

   

   

or,

   

   

∴ the general solution is