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

Solve sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta .

Solve : 3-2 cos theta -4 sin theta - cos 2theta+sin 2theta=0 .

Solve 7cos^2theta+3sin^2theta=4

If (x)/(cos theta)=(y)/(cos(theta-(2pi)/(3)))=(z)/(cos(theta+(2pi)/(3))), then x+y+z=

Prove that cos theta +cos ((2pi)/(3)-theta)+cos ((2pi)/(3)+theta)=0

Prove that cos theta + cos ((2pi)/(3)- theta)+ cos ((2pi)/(3)+ theta)=0

IF tan ( pi cos theta) = cot ( pi sin theta ) then cos ( theta - (pi)/(4)) is equal to

Solve the equations: tan theta + tan (theta + (pi)/(3)) + tan (theta + (2pi)/(3)) = sqrt(3)