Prove that,
`cos alpha + cos(120^(@) + alpha) + cos (120^(@) - alpha) = 0`

Prove that cos alpha cos (120^(@) + alpha) cos (240^(@) + alpha) = 1/4 cos 3 alpha

I : If x cos theta = y cos (120^@ + theta ) = z cos ( theta + 240^(@)) then xy+ yz+ zx=1 II : cos alpha + cos (120^(@) + alpha ) + cos (120^@ - alpha ) =0

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

Prove that, cos^(3) alpha + cos^(3) (120^(@) + alpha) + cos^(3) (240^(@) + alpha) = 3/4 cos 3 alpha

Prove that sin alpha + sin (120^(@) + alpha) + sin(240^(@)+ alpha)=0

Prove that : sec alpha+ sec (120^(@)+ alpha) sec (120^(@)-alpha)=-3 sec 3 alpha

Prove that cos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2