# [ASK] Proving Trigonometry

#### Monoxdifly

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.

#### Idea

Try $$\displaystyle \alpha =\frac{\pi }{4};\beta =\frac{\pi }{4};\gamma =\frac{\pi }{2}$$

topsquark

#### Monoxdifly

Is there any other way besides trial and error?

#### Cervesa

Is there any other way besides trial and error?
just try it ... note what happens

#### Monoxdifly

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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