Let sin^-1x + sin^-1y + sin^-1z = $\frac{3\pi}{2}$ for 0 ≤ x, y z ≤ 1. What is the value of x¹⁰⁰⁰ + y¹⁰⁰¹ + z¹⁰⁰²?

What is the value of following?

$\rm cot \left[sin^{-1} \frac{3}{5}+cot^{-1}\frac{3}{2} \right]$

What is the slope of the tangent of y = cos^-1 (cos x) at x = $-\frac{\pi}{4}$?

$\rm tan^{-1}x+cot^{-1}x=\frac{\pi}{2}$ holds, when