how would you varify the following
sinx+sinx cot^2x=cscx
The same way you do any of these proofs. Start using the trig identities you know, to transform one side of the equation till it matches the other side. I used to love these identity proofs when I studied trig. It was amazing how many ways there were to write the same things!
Do lots of them. It will stand you in good stead later on.
But I digress.
sin + sin cot^2
sin (1 + cot^2)
sin(csc^2)
1/csc * csc^2
csc