Problem

Problem

If xi∈[0,1]∀i=1,2,3,…,28x_i \in [0, 1] \forall i = 1, 2, 3, \dots, 28 then find the maximum value of sin⁡−1x1cos⁡−1x2+sin⁡−1x2cos⁡−1x3+sin⁡−1x3cos⁡−1x4+⋯+sin⁡−1x28cos⁡−1x1\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} + \dots + \sqrt{\sin^{-1} x_{28}} \sqrt{\cos^{-1} x_1}

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