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Question

If α=cos α+i sin α,b=cos β+i sin β,c=cos γ+isin γ and bc+ca+ab=1 then cos(βγ)+cos(γα)+cos(αβ)isequalto
  1. 0
  2. 1


Solution

The correct option is B 1
bc=cos β+isin βcos γ+isin γ×cos γisin γcos γisin γ
bc=cos(βγ)+isin(βγ)                      ......(i)
        Similarly,  ca=cos(γβ)+sin(αβ)   ......(ii)
         and ab=cos(αβ)+isin(γβ)     .....(iii)
        from (i) + (ii) + (iii)
   cos(βγ)cos(γα)+cos(αβ)+i[sin(βγ)+som(γα)+sin(αβ)]=1 
Equating real and imaginary parts,
cos(βγ)+cos(γα)+cos(αβ)=1     
 

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