separation of variabes,new constant help needed

I have separated the variables of dy/dx +2ycot2x = 0

By taking -1/2y to the left i ended u with

y = 1/2Asin2x i. 1/2Acosec2x where A in a constant, my question in since the mark scheme gives 1/Acosec2x can i make a new constant B from the 2A which would represent the right answer in the mark scheme?

If not i believe there may be something i'm missing at the stage

-0.5ln2y = 0.5lnsin2x + c which would get me the answer. I have an exam tommorow and really worried if someone couldhe me here this would be great thanks!!