If `x , y , z in [-1,1]` such that `sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2,` find the value of `x^2+y^2+z^2`

Explanation

Given that,

`x , y , z in [-1,1]`

`sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2`

`-frac{pi}{2} le sin^(-1) x le frac{pi}{2}`

`sin^(-1) x=sin^(-1) y=sin^(-1) z=-frac{pi}{2}`

`sin(sin^(-1) x)=sin(-frac{pi}{2})`

`x=-1, y=-1, z=-1`

`x^2+y^2+z^2=(-1)^2+(-1)^2+(-1)^2=1+1+1=3`


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