If ∑i=12n sin−1xi=nπ, then ∑i=12n xi is equal to
n
2n
n(n+1)2
none of these
We have, ∑i=12n sin−1xi=nπ
⇒sin−1x1+sin−1x2+…+sin−1x2n=nπ
Let sin−1x1=α1,sin−1x2=α2,…,sin−1xn=αn
∴α1+α2+…+α2n=nπ ……… (1)
⇒x1=sinα1,x2=sinα2,…,x2n=sinα2n
∴∑i=12n xi=x1+x2+…+x2n=sinα1+sinα2+…+sinα2n
Clearly, from (1), α1=π2,∀i=1,2,…,2n
∴ ∑i=12n xi=1+1+…+1⏟2n times =2n