Greatest value

If xi>0 for 1≤i≤n and x1+x2+....+xn=π ,then find greatest value of sinx1+sinx2+.......+sinxn

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62
Lokesh Verma ·

use jensen's inequality to get

sinx1+sinx2+.......+sinxnn<= sin{(x1+x2+...xn)/n}

thus the answer is n sin(Ï€/n)

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