`cos theta + cos (240^(@) + theta ) + cos (240^(@)- theta )=`

Prove that cos theta + cos (120^(@) + theta) + cos ( 120^(@)-theta) =0. Hence deduce that cos ^(3) theta + cos ^(3) ( 120^(@) + theta ) + cos^3( 120^(@)-theta) = 3/4 cos 3 theta.

sin ( 240^(@) + theta) + cos (330^(@) + theta ) = 0

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 theta+cos(120^(@)+theta)+cos(240^(@)+theta)=0

cos A + cos (240^(@) +A)+ cos (240^(@)-A)=

Statement I: If x cos theta=y cos(120^(@)+theta)=z cos(theta+240^(@)) then xy+yz+zx=1 Statement II: cos alpha+cos(120^(@)+alpha)+cos(120^(@)alpha)=0 Which of the above statements is correct

cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n theta=

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1