Question

If ${\sum }_{i-l}^{2n}co{s}^{-1}{x}_i=0$, then ${\sum }_{i-l}^{2n}co{s}^{-1}{x}_i$ is

• A. n
• B. 2n
• C. n(n+1)/2
• D. 3n

Answer 1

The correct option is B

2n

Since, $0\le co{s}^{-1}{x}_i\le \pi ,\therefore co{s}^{-1}{x}_i=0$ for all i
$\therefore x_i=1$ for all i $\therefore {\sum }_{i-l}^{2n}co{s}^{-1}{x}_i=2n$