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Trignometry

Cool goIITian

Joined:	18 Feb 2009
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21 Feb 2009 08:36:01 IST

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Find max. value of sinA + sinB + sinC if A B C are angles of a triangle. I know its 3sqrt(3)/2. usin

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Find max. value of sinA + sinB + sinC if A B C are angles of a triangle. I know its 3sqrt(3)/2. using symmetry, but try proving algebraically.

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Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 5524

21 Feb 2009 13:22:47 IST

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Algebrically itis problem of maximising a function of two variables.If angle A = x and angle B = y then angle C = 180-x-ySo f(x,y) = sin(x) + cos(x) + sin(x+y)diff wrt to x (taking partial derivative and putting it equal to 0 we get)cos(x)+cos(x+y) = 0Similarly cos(y) + cos(x+y) = 0That gives cos(x) = cos(y) = -cos(x+y)This is true for x= y = 60 degree

Soumik

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Joined: 31 Jul 2008

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11 May 2012 22:03:11 IST

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try out jenson's inequality

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