If #sum_(i=1)^(n) cos(A_i) = n# then find #sum_(i=1)^(n) sin(A_i)#?

1 Answer
Ananda Dasgupta
Jul 2, 2018

0 (assuming all the #A_i#s are real)

Explanation:

Since the maximum value of #cos(A)_i# for real #A_i# is 1, the sum of #n# such numbers can be #n# if and only if each one of them is equal to 1. Thus

#cos(A_i) = 1,qquad i=1,2,...,n implies#

#sin(A_i) = sqrt(1-cos^2(A_i))=0,qquad i=1,2,...,n#

Thus, the required sum is 0.

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