Prove the following to be an identity

Question

(cotx + cscx)*(1-cosx)=sin x

Answer 1

(cos/sin + 1/sin)(1-cos)
=(cos/sin+1/sin)(1)+(cos/sin+1/sin)(-cos)
= cos/sin+1/sin-cos^2/sin-cos/sin
= (1/sin )(1-cos^2) but 1-cos^2=sin^2
so
sin^2/sin
= sin

Answer 2

sin isnt an identity to begin with

and i got sin^2 x + cos^2 x = 1
the ansswer says its what i got

Answer 3

The right hand side says sin x
You must make the left hand side come out sin x
That is what I did

Yes, I also used sin^2 + cos^2 = 1
in saying
1 - cos^2 = sin^2