SOLUTION: help verifying the identity sin^2(theta/2)=csc(theta)-cot(theta)/2csc theta

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Question 154116: help verifying the identity
sin^2(theta/2)=csc(theta)-cot(theta)/2csc theta
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Note that I have used the Greek letter "alpha" instead of "theta", because the letter "theta" can not display properly here
The right hand side of the identity is
RHS=%28csc+%28alpha%29-cot+%28alpha%29%29%2F%282csc+%28alpha%29%29
=%281%2Fsin%28alpha%29-cos%28alpha%29%2Fsin%28alpha%29%29%2F%282%2Fsin%28alpha%29%29
=%28%281-cos%28alpha%29%29%2Fsin%28alpha%29%29%2A%28sin%28alpha%29%2F2%29%29
=
=%281-cos%28alpha%29%29%2F2
=%281-%281-2sin%5E2%28alpha%2F2%29%29%29%2F2
=%281-1%2B2sin%5E2%28alpha%2F2%29%29%2F2
=%282sin%5E2%28alpha%2F2%29%29%2F2
=%28cross%282%29sin%5E2%28alpha%2F2%29%29%2Fcross%282%29
=sin%5E2%28alpha%2F2%29%29