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Trignometry

Cool goIITian

 Joined: 18 Feb 2009 Post: 89
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
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

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.

Forum Expert
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

Blazing goIITian

Joined: 31 Jul 2008
Posts: 1266
11 May 2012 22:03:11 IST
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try out jenson's inequality

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