Remember that the cosecant is the reciprocal of the sine. CSC(x) = 1/SIN(x).
Now operate on the left side, and see if you can make it look like the right side:
CSCx (1 + SINx)
Substitute for CSCx :
(1/SINx) (1 + SINx)
Multiply them:
1/SINx + SINx/SINx
which is the same as 1/SINx + 1
which is the same as CSCx + 1,
and that's the right side of the identity, so you proved it.
