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# help

0
206
5

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

Oct 4, 2019

#1
+6179
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$$\text{The answer appears to be \dfrac 1 2(1+\sqrt{5})}$$

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Oct 4, 2019
#2
+108682
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How did you reach that conclusion Rom?

Melody  Oct 4, 2019
#3
+6179
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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
+29249
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Here's a possible derivation:

Oct 4, 2019
#5
+108682
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Thanks Rom and Alan

Oct 4, 2019