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If $\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \frac{π}{6},$ then value of $\frac{x^{2}}{4} - \frac{x y}{2 \sqrt{3}} + \frac{y^{2}}{9}$ is

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Correct option is C

We have cos−1x2+cos−1y3=π6⇒cos-1xy6-1-x241-y29=π6 ⇒xy6-1-x241-y29=cosπ6=32 ⇒xy6-32=1-x241-y29 ⇒xy6-322=1-x241-y29 ⇒x24-xy23+y29=14

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If cos−1x2+cos−1y3=π6,then value of x24−xy23+y29 is

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If $\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \frac{π}{6},$ then value of $\frac{x^{2}}{4} - \frac{x y}{2 \sqrt{3}} + \frac{y^{2}}{9}$ is