Question

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

• A. \N
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A \N

We know that $|si{n}^{-1}x|⩽\frac{\pi }{2}$
Therefore, $si{n}^{-1}x+si{n}^{-1}y+si{n}^{-1}z=\frac{3\pi }{2}$
$\Rightarrow si{n}^{-1}x=si{n}^{-1}y=si{n}^{-1}z=\frac{\pi }{2}$
$\Rightarrow x=y=z=sin\frac{\pi }{2}=1$
$\Rightarrow x^{100}+y^{100}+z^{100}-\frac{9}{x^{101}+y^{101}+z^{101}}=3-\frac{9}{3}=0$