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If vec(a) and vec(b) are unit vectors in...

If `vec(a)` and `vec(b)` are unit vectors inclined at an angle `theta` then prove that (i)`sin(theta/2)=1/2|vec(a-vec(b)|` (ii) `tan(theta/2)=(|vec(a)-vec(b)|)/(|vec(a)-vec(b)|)`

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Here, `veca` and `vecb` are unit vectors.
`:. |hata| = |hatb| = 1`
(i)`|hata-hatb|^2 = (hata)^2+(hatb)^2-2hata*hatb`
`=|hata|^2+|hatb|^2-2|hata||hatb|cos theta`
`=1^2+1^2-2(1)(1)costheta`
`=>|hata-hatb|^2=2(1-costheta)`
`=>|hata-hatb|^2/2 = 1-costheta`
...
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