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If $\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = θ$ then $9 x^{2} - 12 x y \cos θ + 4 y^{2}$ is equal to

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−36sin2⁡θ

36sin2⁡θ

36cos2⁡θ

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detailed solution

Correct option is C

We have,cos−1⁡x2+cos−1⁡y3=θ⇒cos−1⁡xy6−1−x241−y29=θ⇒xy−4−x29−y2=6cos⁡θ⇒(xy−6cos⁡θ)2=4−x29−y2⇒−12xycos⁡θ+36cos2⁡θ=36−4y2−9x2⇒9x2+4y2−12xycos⁡θ=36sin2⁡θ

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If cos−1⁡x2+cos−1⁡y3=θ then 9x2−12xycos⁡θ+4y2 is equal to

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If $\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = θ$ then $9 x^{2} - 12 x y \cos θ + 4 y^{2}$ is equal to