" 5."cos^(2)alpha+cos^(2)(alpha+120^(@))+cos^(2)(alpha-120^(@))=(3)/(2)

cos ^(2) alpha + cos ^(2) (alpha + 120^(@)) + cos ^(2) (alpha - 120^(@)) is equal to

cos ^(2) alpha + cos ^(2) (alpha + 120^(@)) + cos ^(2) (alpha - 120^(@)) is equal to

Show that, cos^(2)alpha + cos^(2) (120^(@) - alpha) + cos^(2) (120^(@) + alpha) = 3/2.

Assertion (A):cos^(2)theta+cos^(2)(60^(@)-theta)+cos^(2)(60^(@)+theta)=(3)/(2)sin alpha-sin(120^(@)-alpha)+sin(120^(@)+alpha)=0

Assertion (A):cos^(2)theta+cos^(2)(60^(@)-theta)+cos^(2)(60^(@)+theta)=(3)/(2)sin alpha-sin(120^(@)-alpha)+sin(120^(@)+alpha)=0

cos alpha+cos(120^(@)+alpha)+cos(120^(@)-alpha)=0

To prove ((1)/(sec^(2)alpha-cos^(2)alpha)+(1)/(cos ec^(2)alpha-sin^(2)alpha))cos^(2)alpha sin^(2)alpha=(1-sin^(2)alpha cos^(2)alpha)/(2+sin^(2)alpha cos^(2)alpha)

cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2alpha cos2beta=

((1)/(sec^(2)alpha-cos^(2)alpha)+(1)/(cos ec^(2)alpha-sin^(2)alpha))cos^(2)alpha*sin^(2)alpha=(1-cos^(2)alpha*sin^(2)alpha)/(2+cos^(2)alpha*sin^(2)alpha)