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Saturday, April 21, 2018

maximum minimum of function

For $A,B,C$ non-negative angles such that $A+B+C = \pi / 2$, find the maximum and minimum of: $$ f = \sin A + \sin B + \sin C + \sin^2 A + \sin^2 B + \sin^2 C$$ and $$g = \cos A (\sin A -1) + \cos B (\sin B - 1) + \cos C (\sin C - 1)$$

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