Question 26174
There are many ways to verify identities.  One way is to change what you can to sine and cosine expressions.
Left side work:
(1/sinx)-(cosx/sinx)=[1-cosx]/sinx
Right side work:
[2(1-cosx)(1+cosx)[/[2sinx+2sinx cosx]=2(1-cosx)(1+cosx)/2sinx(1+cosx)
=(1-cosx)/sinx
Right side equals left side.  This verifies the identity.

Cheers,
Stan H.