[Sami A]

solve the following for 0 is less than or equal to x which is less than or equal to 2pie
sinxcscx-cscx+2sin=0

[dmatos]

First thing to do - try to simplify this equation. Note that cscx = 1/sinx:

sinxcscx = 1

1 - 1/sinx + 2sinx = 0

Well, this looks like it could become a fairly simple quadratic equation with a bit of manipulation. Multiply both sides of the equation by sinx. Then, let y=sinx, and you should see a nice quadratic equation in y.

Solve the quadratic equation for y (you'll get 2 answers). Then, you have sinx = y. Solve this (I believe the numbers are straightforward - use the inverse trig functions on the calculator if you don't recognize the values). I'm pretty sure the two possible values for y give me three possible values for x that lie between 0 and 2pi (mmm... pie... )

Hope that helps!