Question
If a=cosα+isinα, b=cosβ+isinβ,
c=cosγ+isinγ and bc+ca+ab=1,Then
cos(β-γ)+cos(γ-α)+cos(α-β) is equal to
c=cosγ+isinγ and bc+ca+ab=1,Then
cos(β-γ)+cos(γ-α)+cos(α-β) is equal to
Answer: Option D
:
D
bc=cosβ+isinβcosγ+isinγ×cosγ−isinγcosγ−isinγ
⇒bc=cos(β−γ)+isin(β−γ).....(i)
Similarly,ca=cos(γ−α)+isin(γ−α).......(ii)
And ab=cos(α−β)+isin(α−β).......(ii)
Equating real and imaginary parts,
cos(β−γ)+cos(γ−α)+cos(α−β)=1
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:
D
bc=cosβ+isinβcosγ+isinγ×cosγ−isinγcosγ−isinγ
⇒bc=cos(β−γ)+isin(β−γ).....(i)
Similarly,ca=cos(γ−α)+isin(γ−α).......(ii)
And ab=cos(α−β)+isin(α−β).......(ii)
Equating real and imaginary parts,
cos(β−γ)+cos(γ−α)+cos(α−β)=1
Was this answer helpful ?
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