If `cos2 theta =0`,determine`|(0,cos theta,sin theta),(cos theta ,sin theta,0),(sin theta,0,cos theta)|^(2)`

determinant |"cos theta sin theta -sin theta cos theta

Prove the orthogonal matrices of order two are of the form [(cos theta,-sin theta),(sin theta,cos theta)] or [(cos theta,sin theta),(sin theta,-cos theta)]

If cos theta{:((cos theta, sin theta),(-sin theta, cos theta)):}+ sin theta{:((x,-cos theta),(cos theta, x)):}=I_(2) , find x.

Find |A| if A= [(0,cos theta_(1),sin theta_(1)),(cos theta_(1),0,sin theta_(2)),(sin theta_(1),-sin theta_(2),0)]

Solve cos theta+cos 2theta+cos 3theta=0 .

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0