Solve the equation tan x = sin x if x is in ( 0, 2pi ).

tanx = sinx is the given equation to solve  for
x:

Solution:

Tanx = sinx/cosx,
by definition. Substitute this in the given equation.

So
the give equation becomes:

sinx/cosx =
sinx.

Divide both sides by
sinx.

1/cosx = 1.

Cross
multiply.

1 = cosx

cosx = 1
when x = 0 or 2npi, n =
0,1,2....

Therefore,

x = 2npi,
n =0 ,  1 ,2 ,3, ....