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

Sin^ 1x+sin^ 1y+sin^ 1z=3π/2 We know that | sin^ 1x |≤π/2 sin^ 1x = sin^ 1y = sin^ 1z = π/2 x = y = z = sinπ/2 = 1 x^100+y^100+z^100 9/x^101+y^101+z^101 = 3 ...

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Byju's Answer

Standard XIII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

sin-1x+sin-1y...

Question

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

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Solution

The correct option is A
0

$s i n^{- 1} x + s i n^{- 1} y + s i n^{- 1} z = \frac{3 π}{2}$
We know that $∣ ∣ s i n^{- 1} x ∣ ∣ \leq \frac{π}{2}$
$s i n^{- 1} x = s i n^{- 1} y = s i n^{- 1} z = \frac{π}{2}$
$x = y = z = s i n \frac{π}{2} = 1$
$x^{100} + y^{100} + z^{100} - \frac{9}{x^{101} + y^{101} + z^{101}} = 3 - \frac{9}{3} = 0$

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Q. lf

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

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

Q. 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}}

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