If sin-1x-sin-1y-sin-1z-3-2- then the value of x100-y100-z100-9x101-y101-z101 is

The correct option is A 0 Given, sin^ 1x+sin^ 1y+sin^ 1z=3π2 This will only possible when sin^ 1x=sin^ 1y=sin^ 1z=π2 Since sin^ 1x∈ [ π2,π2] ...

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Standard XII

Mathematics

Algebra of Derivatives

If sin-1x+s...

Question

If ${sin}^{- 1} x + {sin}^{- 1} y + {sin}^{- 1} z = \frac{3 π}{2}$ , then the value of $x^{100} + y^{100} + z^{100} - \frac{9}{x^{101} + y^{101} + z^{101}}$ is

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Solution

The correct option is A $0$
Given, $s i n^{- 1} x + s i n^{- 1} y + s i n^{- 1} z = \frac{3 π}{2}$

This will only possible when $s i n^{- 1} x = s i n^{- 1} y = s i n^{- 1} z = \frac{π}{2}$

Since $s i n^{- 1} x \in [\frac{- π}{2}, \frac{π}{2}]$

then $= s i n \frac{π}{2} = 1 ⟹ x = y = z = 1$

Hence desired value is = $1 + 1 + 1 + (\frac{- 9}{1 + 1 + 1}) = 3 - \frac{9}{3} = 0$

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Similar questions

$s i n^{- 1} x + s i n^{- 1} y + s i n^{- 1} z = \frac{3 π}{2},$ then the value of $x^{100} + y^{100} + z^{100} - \frac{9}{x^{101} + y^{101} + z^{101}} =$

Q. lf

{sin}^{- 1} x + {sin}^{- 1} y + {sin}^{- 1} z = \frac{3 π}{2}

, then

x^{100} + y^{100} + z^{100} - \frac{9}{x^{101} + y^{101} + z^{101}} =

$s i n^{- 1} x + s i n^{- 1} y + s i n^{- 1} z = \frac{3 π}{2},$ then the value of $x^{100} + y^{100} + z^{100} - \frac{9}{x^{101} + y^{101} + z^{101}} =$