SOLUTION: if alpha +beta + gamma = 0 , then prove that sin2α+sin2β+sin2γ=2(sinα+sinβ+sinγ)(1+cosα+cosβ+cosγ)

Algebra ->  Trigonometry-basics -> SOLUTION: if alpha +beta + gamma = 0 , then prove that sin2α+sin2β+sin2γ=2(sinα+sinβ+sinγ)(1+cosα+cosβ+cosγ)      Log On


   

Question 1005148: if alpha +beta + gamma = 0 , then prove that sin2α+sin2β+sin2γ=2(sinα+sinβ+sinγ)(1+cosα+cosβ+cosγ)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
By expanding the right-hand side (RHS) we can invoke a lot of trig identities:


using the fact that .

Since , we have that , etc., so we can simplify as follows: