If `sin^(-1)x_i in [0,1]AAi=1,2,3, .28` then 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)+` `sqrt(sin^(-1)x_3)sqrt(cos^(-1)x_4)++sqrt(sin^(-1)x_(28))sqrt(cos^(-1)x_1)`

Explanation

To solve the problem, we need to find the maximum value of the expression:

\[ E = \sqrt{\sin^{-1} x_1} \sqrt{\cos^{-1} x_2} + \sqrt{\sin^{-1} x_2} \sqrt{\cos^{-1} x_3} + \ldots + \sqrt{\sin^{-1} x_{28}} \sqrt{\cos^{-1} x_1} \]

where \( \sin^{-1} x_i \) is in the interval \([0, 1]\) for \( i = 1, 2, \ldots, 28\).

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