statement-I- `cos^3alpha + cos^3(alpha+2pi/3) + cos^3(alpha+4pi/3) = ``3cosalpha cos(alpha+2pi/3)cos(alpha+4pi/3) Because` Statement-II - `if a+b+c=0 iff a^3+b^3+c^3=3abc`

statement-I- cos^(3)alpha+cos^(3)(alpha+2(pi)/(3))+cos^(3)(alpha+4(pi)/(3))=3cos alpha cos(alpha+2(pi)/(3))cos(alpha+4(pi)/(3))Because Statement-II -0hArr a^(3)+b^(3)+c^(3)=3abc if a+b+c=0hArr a^(3)+b^(3)+c^(3)=3abc

sin alpha+sin(alpha+((2pi)/3))+sin(alpha+((4pi)/3))=0

Eliminating alpha from xcos alpha = y cos(alpha +2pi/3) = zcos (alpha +4pi/3) establish that xy + yz + zx= 0

(cos alpha + (cos ((2 pi) / (3) + alpha)) + cos ((4 pi) / (3) + alpha))

Prove that: cos^(3)A + cos^(3)((2pi)/(3)+A) + cos^(3)((4pi)/3+A) = 3/4 cos3A

sin alpha-sin2 alpha+sin3 alpha=4cos(3 alpha)/(2)cos alpha sin(alpha)/(2)

cos2 alpha-cos3alpha-cos4alpha+cos5alpha simplifies to :