x=\cos \alpha+i\sin \alpha, y=\cos \beta+i\sin \beta, z=\cos \gamma+i\sin \gamma\ \text{and}\

Kamren Franco

Kamren Franco

Answered question

2022-01-30

x=cosα+isinα,y=cosβ+isinβ,z=cosγ+isinγ and x+y+z=xyz. Prove that cos(βγ)+cos(γα)+cos(αβ)=1?

Answer & Explanation

bekiffen32

bekiffen32

Beginner2022-01-31Added 8 answers

This proposition is false, e.g. when α=0,β=π2,γ=π2
Explanation:
{α=0β=π2γ=π2
Then:
{x=1y=iz=i
and x+y+z=1+ii=1=1i(i)=xyz
With these values, we find:
cos(βγ)+cos(γα)+cos(αβ)
=cos(π)+cos(π2)+cos(π2)
=1+0+0=11

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