If `Sigma_(r=1)^(n) cos^(-1)x_(r)=0, then Sigma_(r=1)^(n) x_(r)` equals

Options

A. 0
B. n
C. `(n(n+1))/(2)`
D. none of these

Explanation

We know that
`0lecos^(-1)x_(r )lepi,r=1,2,.n`
`therefore underset(r=1)overset(n)Sigma cos^(-1) x_(r ) =0`
`rarr cos^(-1)x_(r ) =0 for r=1,2..n`
`rarr cos^(-1)x_(r)=0 for r=1,2..n`
`rarr x_(r ) =1 for r=1,2,…n `
`therefore underset(r=1)overset(n)Sigma x_(r )=underset(r=1)overset(n)Sigma1=n`