If for all , find the maximum value of ^ -1 x_1 ^ -1 x_2 + ^ -1 x_2 ^ -1 x_3 + + ^ -1…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

x_i\in[0,1]

for all

i=1,2,3,\ldots,28

, find the maximum value of

\sqrt{\sin^{-1}x_1}\sqrt{\cos^{-1}x_2}+\sqrt{\sin^{-1}x_2}\sqrt{\cos^{-1}x_3}+\cdots+\sqrt{\sin^{-1}x_{28}}\sqrt{\cos^{-1}x_1}.