Question

Find all solutions on the interval (0,2pi)
tan x sin2 x= tan x

Answer 1

If tan(x)=0 then the equation works.

You can also go about it this way:
tan(x)sin(2x)=tan(x)
Divide both sides by tan(x)
sin(2x)=1
Let u=2x

Answer 2

tan x(sin2x -1) =0 (DO NOT CROSS OUT THE TAN X!!!)
=> tan x = 0 or sin 2x = 1