I am a new user of Mathematica and in this small work, copied from an example, the last output should be 0, but it is not in mine paper. Can anyone see the mistake? I suppose the problem is in a definition.
Take a look at your code. Do you see how the function "sin" is blue instread of black? This means it is not defined.
Built-in functions are always capitalized. So it should be "Sin" instead of "sin".
That is the start of what is probably wrong here. What domain are you Simplifying over? Is this equation supposed to be true for Real values or Complex Values? Are there any assumptions about the values of some of the variables? These should built into the code using "Assuming"