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)]`

Show that every 2 -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]]

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)]

(i) |(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-sin theta)/cos theta

" (1) "|[cos theta,-sin theta],[sin theta,cos theta]|

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

Find the value of |[cos theta,-sin theta],[sin theta,cos theta]|

(sin 3theta)/(sin theta)-(cos 3theta)/(cos theta)=

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