Prove that all values of theta: `|(sintheta, costheta, sin2theta),(sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin (2theta+(4pi)/3)),(sin (theta- (2pi)/3), cos (theta- (2pi)/3), sin (2theta- (4pi)/3))|=0`

The value of the determinant |sin theta,cos theta,sin2 thetasin(theta+(2 pi)/(3)),cos(theta+(2 pi)/(3)),sin(2 theta+(4 pi)/(3))sin(theta-(2 pi)/(3)),cos(theta-(2 pi)/(3)),sin(2 theta-(4 pi)/(3))

Prove that: 4sin theta sin(theta+(pi)/(3))sin(theta+(2 pi)/(3))=sin3 theta

If x sintheta=ysin(theta+(2pi)/(3))=z sin(theta+(4pi)/(3)), then

The volume of the parallelepiped whose coterminous edges are represented by the vectors 2vecb xx vecc, 3vecc xx veca and 4veca xx vecb where veca=(1+sintheta)hati+costhetahatj+sin2thetahatk , vecb=sin(theta+(2pi)/(3))hati+cos(theta+(2pi)/(3))hatj+sin(2theta+(4pi)/(3))hatk , vecc=sin(theta-(2pi)/(3))hati+cos(theta-(2pi)/(3))hatj + sin(2theta-(4pi)/(3))hatk is 18 cubic units, then the values of theta , in the interval (0,pi/2) , is/are

If 2 sin(theta+(pi)/(3))=cos(theta-(pi)/(6)) , then tantheta =

Prove that sin(theta-(pi)/(6))+cos(theta-(pi)/(3))=sqrt(3)sin theta

If 0

4 sin ((pi)/(3) + theta)sin ((pi)/(3)- theta)=

Prove that 4sin theta sin((pi)/(3)+theta)sin((2 pi)/(3)+theta)=sin3 theta