Find all possible values of x and y for which `cos^(-1)sqrtx+cos^(-1)sqrt(1-x)+cos^(-1)sqrt(1-y)=((3pi)/4)`

Explanation

`cos^(-1)sqrtx=cos^(-1)sqrt(1-x)=cos^(-1)sqrtx+sin^(-1)sqrtx=pi/2`
The given equation can be rewritten as
`pi/2+cos^(-1)sqrt(1-y)=(3pi)/4`
`rArr cos^(-1)sqrt(1-y)=pi/4`
`sqrt(1-y)=1/sqrt2`
`rArr 1-y=1/2`
`rArry=1-1/2=1/2`
For `cos^(-1)sqrtx` to be defined `-1 le sqrtx le 1`
But `sqrtx` by definition, is non-negative i.e., `sqrtx ge0`
Combining the two `0 le sqrtx le 1i.e., 0 le xle1`
Thus the possible values of x, y are `0 le x le 1, y=1/2`