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Michelle Mendoza

Michelle Mendoza

Answered question

2022-06-29

Given,
cos ( β γ ) + cos ( γ α ) + cos ( α β ) = 3 2
Prove that:
1. cos α + cos β + cos γ = 0
2. sin α + sin β + sin γ = 0

Answer & Explanation

Jenna Farmer

Jenna Farmer

Beginner2022-06-30Added 17 answers

You have
cos ( β γ ) + cos ( γ α ) + cos ( α β ) = 3 2
From this we have
2 ( cos α cos β + cos β cos γ + cos γ cos α ) + 2 ( sin α sin β + sin β sin γ + sin γ sin α ) = 3 ( c y c l i c cos 2 α + c y c l i c sin 2 α ) ( c y c l i c cos α ) 2 + ( c y c l i c sin α ) 2 = 0.
So,
c y c l i c cos α = 0 , and c y c l i c sin α = 0

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