How do you simplify #sin(theta/2)# using the double angle identities?

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Answer 1 · 2017-06-05T06:14:27

The answer is #=+-sqrt((1-costheta)/2)#

We need

#cos2theta=1-2sin^2(theta)#

So,

#costheta=1-2sin^2(theta/2)#

#2sin^2(theta/2)=1-costheta#

#sin^2(theta/2)=(1-costheta)/2#

#sin(theta/2)=+-sqrt((1-costheta)/2)#