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

1 Answer
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)