Question

If $\sum _{i=1}^{10}{\cos }^{-1}{x}_i=0$, then $\sum _{i=1}^{10}{x}_i$ is

• A. $0$
• B. $10$
• C. $5$
• D. none of these

Answer 1

The correct option is B $10$

The above expression can be written as
$co{s}^{-1}\left(x_1\right)+co{s}^{-1}\left(x_2\right)+co{s}^{-1}\left(x_3\right)+...co{s}^{-1}\left(x_{10}\right)=0$
We know that $co{s}^{-1}\left(1\right)=0$
Hence
$x_1=x_2=...=x_{10}=1$
Therefore
$x_1+x_2+...+x_{10}$
$=1+1+1+\mathrm{1...}+1$
$=10\left(1\right)$
$=10$