How Do You Solve These Trigonometric Contest Questions?

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SUMMARY

The discussion focuses on solving two trigonometric contest questions involving triangle ABC and specific angle relationships. The first question examines the condition sin[2*(alfa)]=2sin[beta]*cos[gama], prompting debate on whether an equilateral triangle is the sole solution. The second question involves proving the identity sin(alfa+beta)=2ab/(a^2+b^2) given the equation acos[alfa] + bsin[alfa]=acos[beta]+b[sin[beta]. Participants express skepticism about the effectiveness of hints provided for the second problem.

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1) What kind of triangle is ABC if for his angles we have:
sin[2*(alfa)]=2sin[beta]*cos[gama]

2) If acos[alfa] + bsin[alfa]=acos[beta]+b[sin[beta] , prove that sin(alfa+beta)=2ab/(a^2+b^2)
 
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For question #1,are u sure that equilateral triangle is the only possibble sollution...?

Daniel.
 
I wanted to tell u that the "HINT" for the second problem would have led nowhere...

Daniel.
 

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