Question

If x,y,z∈[−1,1] such that sin−1x+sin−1y+sin−1z=3π2, find the value of x2006+y2007+z2008−9x2006+y2007+z2008

Answer 1

Answer:

-8018.

Step-by-step explanation:

Since the range of $sin^-^1x$ is $[-\pi / 2, \pi / 2]$, therefore, by boundedness, all x, y and z are equal to 1, to satisfy the given condition.

Hence, the value of the given expression is:

2006 + 2007 + 2008 - 9 * 2006 + 2007 + 2008 = -8018.