You can put this solution on YOUR website!
The best way to handle trig identities is to convert everything to sine and cosine.
It is always best to start with the hardest side but in this case, it makes no difference because both sides of the equation are complicated.
Here is the conversion:
cotx = cosx/sinx
cscx = 1/sinx
I will set it up and you can finish.
[(cosx/sinx)]/[(1/sinx) + 1)] = [(1/sinx) - 1)]/(cosx/sinx)
This ugly thing is just a complex fraction.
Can you take it from here?