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

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Answer 1 · 2018-05-08T00:25:39

#cos(x/2)=+-sqrt((1+cosx)/2)#

#cos2x=2cos^2x-1#

use substitution

#theta=2x#

#+1+cosx=2cos^2(x/2)cancel(-1+1#

#(1+cosx)/2=(cancel2cos^2(x/2))/cancel2#

#+-sqrt((1+cosx)/2)=sqrt(cos^cancel2(x/2)#

#cos(x/2)=+-sqrt((1+cosx)/2)#