Show that every 2-rowed real orthogonal matrix is of any one of the forms `[(cos theta,-sin theta),(sin theta,cos theta)]` or `[(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)]

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)]

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)]

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)]

Statement 1: If A is an orthogonal matrix of order 2, then |A|=+-1. Statement 2: Every two-rowed real orthogonal matrix is of any one of the forms [[cos theta,-sin thetasin theta,cos theta]] or [[cos theta,sin thetasin theta,-cos theta]]

(cos theta)/(1-sin theta)=(1+cos theta+sin theta)/(1+cos theta-sin theta)

(sin theta-cos theta+1)/(sin theta+cos theta-1)=(1+sin theta)/(cos theta)

(1+cos theta+sin theta)/(1+cos theta-sin theta)=(1+sin theta)/(cos theta)

Simplify : cos theta[(cos theta,sin theta),(-sin theta,cos theta)]=sin theta[(sin theta,-cos theta),(cos theta,sin theta)]

cos theta+sin theta=cos2 theta+sin2 theta