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(β−γ)+cos(γ−α)+cos(α−β)isequalto01

Solution

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

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