If ` hat a` and ` hat b` are unit vectors inclined at an angle `theta` , then prove that `costheta/2=1/2| hat a+ hat b|` `tantheta/2=1/2|( hat a- hat b)/( hat a+ hat b)|`

Explanation

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`

`=>|hata+hatb|^2/2 = 2cos^2(theta/2)`

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