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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

A
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C
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Solution

The correct option is C 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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