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If (sin^(-1)x)^2+(sin^(-1)y)^2+(sin^(-1)...

If `(sin^(-1)x)^2+(sin^(-1)y)^2+(sin^(-1)z)^2=3/4pi^2` , find the value of `x^2+y^2+z^2` .

Text Solution

Verified by Experts

The correct Answer is:
`-3`
`(sin^(-1) x)^(2) + (sin^(-1) y)^(2) + (sin^(-1) z)^(2) = (3pi^(2))/(4)`
`rArr sin^(-1) x = sin^(-1) y = sin^(-1) z = +- (pi)/(2)` ltrbgt for minimum value of `x + y + z, x = y =z = -1`
Hence, `(x + y + z)_("min") = -3`
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