SOLUTION: sin(x)tan(x/2)=1-cosx how to i prove this identity?

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Question 279019: sin(x)tan(x/2)=1-cosx
how to i prove this identity?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29tan%28x%2F2%29=1-cos%28x%29

There are two half-angle identities for tan%28theta%2F2%29

They are 

tan%28theta%2F2%29=sin%28theta%29%2F%281%2Bcos%28theta%29%29

and

tan%28theta%2F2%29=%281-cos%28theta%29%29%2F%28sin%28theta%29%29

We will use the second one:

sin%28x%29tan%28x%2F2%29=1-cos%28x%29

sin%28x%29%28%281-cos%28x%29%29%2Fsin%28x%29%29=1-cos%28x%29

cross%28sin%28x%29%29%28%281-cos%28x%29%29%2Fcross%28sin%28x%29%29%29=1-cos%28x%29

1-cos%28x%29=1-cos%28x%29

Edwin