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If unit vectors A and B are inclined at an angle theta, then prove that IA-BI=2 sin theta/ 2

$W e k n o w t h a t, {| \hat{A} - \hat{B} |}^{2} = (\hat{A} - \hat{B}) . (\hat{A} - \hat{B}) = \hat{A} . \hat{A} + \hat{B} . \hat{B} - 2 \hat{A .} \hat{B} = 1 + 1 - 2 (1) (1) \cos θ = 2 (1 - \cos θ) = 2 [1 - (1 - 2 \sin^{2} θ / 2)] = 4 \sin^{2} θ / 2 | \hat{A} - \hat{B} | = 2 \sin θ / 2$

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