I am confused at what you did on the third line. That is where your error may be.
he multiplied through by sin(x) after bring the 1/sin(x) to the other side
the problem is on the 8th line. when he multiplied through by -1, he forgot to multiply the right hand side. so you should have a -1 on the right
there may be other mistakes, but i stopped checking there. fix it and continue
Yep that was the major problem; line 8. I have most of it now, but still one problem. I have been out of math for a long time and I'm pursuing a Computer Science degree now and I have to go through a lot of math. I skipped Intermediate Algebra, so sometimes I don't remember all the rules.
thanks for the help
that is because 0 is not in the domain of cot(x) or csc(x) either, for that matter. those functions are undefined for x = 0. thus 0 does not work in the original question, and we discard it. (chances are we picked up that erroneous solution when you multiplied through by sin(x)). ALWAYS CHECK YOUR ANSWERS IN THE ORIGINAL QUESTION WHEN DONE