Derivatives

[real wind]

I've got an equation that goes like
x = R * cos(alpha)/sin(alpha)
and then the line after that is
dx/d(alpha) = -R/(sin(alpha))^2

Like this, basically.
I think my teacher wrote it during a lecture, but I don't understand how he got from the first equation to the second one.

I found the derivate in 2 different ways and I got "-1 - (cosx)^2 / (sinx)^2" both times

Maybe he solved it wrong??

Nvm I got it right but he just went a different direction in his answer