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If $\cos^{- 1} x - \cos^{- 1} \frac{y}{2} = α$ then $4 x^{2} - 4 x y \cos α + y^{2}$ is equal to

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a

−4sin2⁡α

b

4sin2⁡α

c

4

d

2sin⁡2α

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detailed solution

Correct option is B

We have,cos−1⁡x−cos−1⁡y2=α⇒ cos−1⁡xy2+1−x21−y24=α⇒ xy2+1−x21−y24=cos⁡α⇒ cos⁡α−xy22=1−x21−y24⇒ cos2⁡α+x2y24−xycos⁡α=1−x2−y24+x2y24⇒ x2+y24−xycos⁡α=sin2⁡α⇒ 4x2−4xycos⁡α+y2=4sin2⁡α

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