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)`

Find all possible values of x and y for which `cos^(-1)sqrtx+cos^(-1)s

1.	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)`
Answer» `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`

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
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