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If the points $O (0, 0), A (\cos α, \sin α),$ $B (\cos β, \sin β)$ are the vertices of a right-angled triangle, then $|\sin (\frac{α - β}{2})| =$

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Correct option is B

We have OA=OB=1and AB=2−2cos⁡(α−β)=2sin⁡α−β2Since ∆AOB is a right triangle. ThereforeAB=OA2+OB2⇒2sin⁡α−β2=2⇒sin⁡α−β2=12

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If the points O(0,0), A(cos⁡α, sin⁡α),B(cos⁡β, sin⁡β) are the vertices of a right-angled triangle, then sin⁡α−β2=

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If the points $O (0, 0), A (\cos α, \sin α),$ $B (\cos β, \sin β)$ are the vertices of a right-angled triangle, then $|\sin (\frac{α - β}{2})| =$