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Among all triangles ABC find the maximum value of \(\sin A + \sin B \sin C.\)

 Oct 4, 2019
 #1
avatar+6045 
+2

\(\text{The answer appears to be $\dfrac 1 2(1+\sqrt{5})$}\)

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 Oct 4, 2019
 #2
avatar+105700 
+1

How did you reach that conclusion Rom?

Melody  Oct 4, 2019
 #3
avatar+6045 
+2

set the Gradient equal to zero and solved (with the help of software) and examined the solutions to see which 

produced a maximum (vice a minimum) and what it was.

 

There's probably some more clever geometric solution here.

Rom  Oct 4, 2019
 #4
avatar+28205 
+4

Here's a possible derivation:

 

 Oct 4, 2019
 #5
avatar+105700 
+1

Thanks Rom and Alan   cool

 Oct 4, 2019

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