Take out variable instead of cancel out in solving equations

How many roots does the equation tan x =2sinx have? For 0<=x<=360 in degree.
sinx/cosx = 2sinx
sinx = 2sinx cosx

Now if you cancel out the term sinx, and the equation becomes 1=2cosx, you will miss 3 answers.

The correct steps are as follow:
0 = 2sinx cosx -sinx
0 = sinx(2cosx -1)
when sinx =0, x can be 0, 180, 360 in degree.
when cosx=0.5, x can be 60, 300 in degree.

There are 5 answers. This technique is very important in both math and A-math. Especially dueling with =0 or trigo problem.