Solve for x the equation cos x-(tan x*cos x)=0, 0

cos(x) - tan(x)*cos(x) =
0

Making use of the fact that tan(x) =
sin(x)/cos(x), we have:

cos(x) -
[sin(x)/cos(x)]/cos(x) = 0

cos(x) - sin(x) =
0

Moving sin(x) to the other side, we can see
that:

cos(x) =
sin(x)

Now ask yourself, where on the unit
circle is cos(x) =
sin(x)?

This occurs only at
pi/4 and 5pi/4.

Note that at pi/2
and 3pi/2, the tan is
undefined.

Therefore, the solution
set is:  {pi/4, 5pi/4}.