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

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– 36 sin2 θ

36 sin2 θ

36 cos2 θ

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Correct option is C

Given, θ=cos−1⁡x2⋅y3−1−x241−y29⇒cos⁡θ=xy6−4−x29−y26⇒(xy−6cos⁡θ)2=4−x29−y2=36−9x3−4y7+x7y7⇒36cos2⁡θ−12xycos⁡θ+4y2+9x2=36∴9x2−12xycos⁡θ+4y2=36sin2⁡θ

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

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Ready to Test Your Skills?

free study material

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