If $\large\overrightarrow a\:and\:\overrightarrow b$ are unit vectors then prove that $\large\frac{1}{2}|\overrightarrow a-\overrightarrow b|=sin\frac{\theta}{2}.$

related to an answer for: If $\hat{a}\;and\;\hat{b}$ are unit vectors inclined at an angle $\theta$,then prove that $$(a)\;\cos \frac{\theta}{2}=\frac{1}{2}|\hat{a}+\hat{b}|\qquad(b)\;\tan \frac{\theta}{2}=\frac {|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}$$

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