[ASK] Proving Trigonometry

Apr 2018
163
38
Sukoharjo
If \(\displaystyle \alpha+\beta+\gamma=180°\), prove that \(\displaystyle 2sin\alpha+2sin\beta+2sin\gamma=4sin\alpha sin\beta sin\gamma\)!
All I knew is that \(\displaystyle sin(\beta+\gamma)=sin(180°-\alpha)=sin\alpha\), but I think it doesn't help in this case.
 
Jun 2013
1,112
590
Lebanon
Try \(\displaystyle \alpha =\frac{\pi }{4};\beta =\frac{\pi }{4};\gamma =\frac{\pi }{2}\)
 
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Apr 2018
163
38
Sukoharjo
Is there any other way besides trial and error?
 
Apr 2018
163
38
Sukoharjo
Well, this was a question asked by a student I am tutoring. He did say that he tried all angles to be 60° and the equation didn't match, so I told him that it means that it couldn't be proved.
 
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