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If sin^(-1)x+sin^(-1)y=pi/3 and cos^(-1)...

If `sin^(-1)x+sin^(-1)y=pi/3` and `cos^(-1)x-cos^(-1)y=pi/6` , find the values of `x` and `y` .

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`cos ^{-1} x-cos ^{-1} y=frac{pi}{6}`

`implies frac{pi}{2}-sin ^{-1} x-frac{pi}{2}+sin ^{-1} y=frac{pi}{6} [therefore cos ^{-1} x=frac{pi}{2}-sin ^{-1} x]`

`implies -(sin ^{-1} x-sin ^{-1} y)=frac{pi}{6} `

`sin ^{-1} x-sin ^{-1} y=-frac{pi}{6}`

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