Question

If $x,y,z\in [-1,1]$ such that ${\cos }^{-1}x+{\cos }^{-1}y+{\cos }^{-1}z=0$, find $x+y+z$.

Answer 1

$\begin{array}{c}{\cos }^{-1}x+{\cos }^{-1}y+{\cos }^{-1}z=0\\ \Rightarrow {\cos }^{-1}x=0\\ \Rightarrow x=1\\ \because {\cos }^{-1}y=0\\ \Rightarrow \therefore y=1\\ \Rightarrow and{\cos }^{-1}z=0\\ \therefore z=0\\ Hence,x+y+z=1+1+1=3.\end{array}$