having trouble with trigonometry , .cscx (1 + sinx) = 1 + cscxprove the identity

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.