solution =0; denominator implies solution different from zero

[vale]

Hello. I want to demonstrate that, when x= 0, then also y = 0. But I have the following equation:
[sin(x)+sin(y-x)-sin(y)]/sin(x)=0
So, I should bring out sin(x)=0, x=0+nTT, but in so doing I exclude the result that I want.
How should I express it correctly?
Thank you!

 

[tkhunny]

sin(0) = 0. Your expression DOES NOT EXIST at x = 0, no matter what sort of manipulation you manage.

If you would like it to be defined at x = 0, you will have to create a piecewise definition.

sin(x)+sin(y-x)-sin(y)]/sin(x)=0 for x NOT 0
0 for x = 0

Maybe that will help you on your way. It's not all that clear what it is you are trying to do.