If #0 < x < phi# , prove that : #sin (x/2) = sqrt((1-cos x)/2)# ?

1 Answer
Nghi N.
Jun 11, 2018

Use trig identity:
#2sin^2 a = 1 - cos 2a#
In this case --> #a = (x/2)#, and 2a = x
We have:
#2sin^2 (x/2) = 1 - cos x#
#sin^2 (x/2) = (1 - cos x)/2#
#sin (x/2) = +- sqrt((1 - cos x)/2#
If #0 < x < pi#, --> #sin (x/2)# is positive -->
#sin (x/2) = sqrt((1 - cos x)/2)#

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