Question

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

Answer 1

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)`