The number of triplets $(x, y, z)$ satisfies the equation $f (x, y, z) = {sin}^{- 1} x + {sin}^{- 1} y + {sin}^{- 1} z = \frac{3 π}{2}$ is

1

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2

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0

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Infinite

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Solution

The correct option is D $1$
As $- \frac{π}{2} \leq {s i n}^{- 1} θ \leq \frac{π}{2}$
And for ${s i n}^{- 1} x + {s i n}^{- 1} y + {s i n}^{- 1} z = \frac{3 π}{2}$
${s i n}^{- 1} x = {s i n}^{- 1} y = {s i n}^{- 1} z = \frac{π}{2}$
$\Rightarrow x = y = z = 1$
Hence option 'A' is correct.

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