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JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

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If the points O(0,0),A(cos⁡α,sin⁡α)O(0,0), A(\cos \alpha, \sin \alpha), B(cos⁡β,sin⁡β)B(\cos \beta, \sin \beta) are the vertices of a right-angled triangle, then ∣sin⁡(α−β2)∣=\left|\sin \left(\frac{\alpha-\beta}{2}\right)\right|=
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Correct option: B
12\frac{1}{\sqrt{2}}
Option B (12\frac{1}{\sqrt{2}}) is correct because the given points form a right-angled triangle, and using the distance formula and trigonometric identities, we can find the value of ∣sin⁡(α−β2)∣\left|\sin \left(\frac{\alpha-\beta}{2}\right)\right|.

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