[" Distance between the points "],[(a cos(theta+(2 pi)/(3)),a sin(theta+(2 pi)/(3)))" and "(a cos(theta+(pi)/(3)),a sin(theta+(vdots)/(3)]

Distance between the points (a cos(theta+((2 pi)/(3))),a sin(theta+((2 pi)/(3)))) and (a cos(theta+((pi)/(3))),a sin(theta+((pi)/(3)))) is

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

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

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))

|(sin theta, cos theta, 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 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))|

tangents are drawn to x^(2)+y^(2)=a^(2) at the points A(a cos theta,a sin theta) and B(a cos(theta+(pi)/(3)),a sin(theta+(pi)/(3))) Locus of intersection of these tangents is

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

Prove that for 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