The value of the determinant `|(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))|`

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

cos theta + sin theta - sin 2 theta = (1)/(2), 0 lt theta lt (pi)/(2)

The volume of the parallelepiped whose coterminous edges are represented by the vectors 2vecb xx vecc, 3vecc xx veca and 4veca xx vecb where 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

For all theta, sin theta + sin(theta + pi)+sin (2pi + theta)=

Prove that tan(theta+(pi)/(6))+cot(theta-(pi)/(6))=(1)/(sin2theta-sin.(pi)/(3))

Solve: sin2theta=sin((2pi)/(3)-theta)

Prove that 4sinthetasin(pi/3+theta)sin((2pi)/3+theta)=sin3theta

If sin(pi cos theta)=cos(pi sin theta) , then sin 2theta=

The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta,0):}|

If sin^(3)theta+sin^(3)(theta+(2pi)/(3))+sin^(3)(theta+(4pi)/(3))=a sinb theta . Find the value of |(b)/(a)| .