If $$cos$$⁡$$A+$$$$cos$$⁡$$B+$$$$cos$$⁡$$C=0$$ and $$cos$$⁡$$3A+$$$$cos$$⁡$$3B+$$$$cos$$⁡$$3C=$$λ$$cos$$⁡Acos⁡Bcos⁡C then λ is

Question

If $$cos$$⁡$$A+$$$$cos$$⁡$$B+$$$$cos$$⁡$$C=0$$ and $$cos$$⁡$$3A+$$$$cos$$⁡$$3B+$$$$cos$$⁡$$3C=$$λ$$cos$$⁡Acos⁡Bcos⁡C then λ is

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If $$cos$$⁡$$A+$$$$cos$$⁡$$B+$$$$cos$$⁡$$C=0$$ then $$cos3$$⁡$$A+cos3$$⁡$$B+cos3$$⁡$$C=3cos$$⁡Acos⁡Bcos⁡C Given $$cos$$⁡$$3A+$$$$cos$$⁡$$3B+$$$$cos$$⁡$$3c=$$λ$$cos$$⁡Acos⁡Bcos⁡$$C4cos3$$⁡A−$$3cos$$⁡$$A+4cos3$$⁡B−$$3cos$$⁡$$B+4cos3$$⁡C−$$3cos$$⁡$$C=$$λ$$cos$$⁡Acos⁡Bcos⁡$$C=4cos3$$⁡$$A+cos3$$⁡$$B+cos3$$⁡C−$$3($$$$cos$$⁡$$A+$$$$cos$$⁡$$B+$$$$cos$$⁡$$C)=4(3cos$$⁡Acos⁡Bcos⁡$$C)$$−$$3(0)=12cos$$⁡Acos⁡Bcos⁡C

$If \cos A + \cos B + \cos C = 0 and \cos 3 A + \cos 3 B + \cos 3 C = λ \cos A \cos B \cos C then λ is$

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If cos⁡A+cos⁡B+cos⁡C=0 and cos⁡3A+cos⁡3B+cos⁡3C=λcos⁡Acos⁡Bcos⁡C then λ is

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$If \cos A + \cos B + \cos C = 0 and \cos 3 A + \cos 3 B + \cos 3 C = λ \cos A \cos B \cos C then λ is$