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If $\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \frac{5 π}{12}$ and $\sin^{- 1} \frac{x}{a} - \sin^{- 1} \frac{y}{b} = \frac{π}{12}$ then $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} =$

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Correct option is D

cos−1xa+cos−1yb=5π12………(1)cos−1yb−cos−1xa=π12……..(2)(1)+(2)⇒cos−1yb=π4⇒yb=12(1)−(2)⇒cos−1xa=π6⇒xa=32∴x2a2+y2b2=54

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If cos−1xa+cos−1yb=5π12and sin−1xa−sin−1yb=π12 thenx2a2+y2b2=

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If $\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \frac{5 π}{12}$ and $\sin^{- 1} \frac{x}{a} - \sin^{- 1} \frac{y}{b} = \frac{π}{12}$ then $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} =$