Simplify `costheta[costhetasinthetasinthetacostheta]+sintheta[sintheta-costhetacosthetasintheta]`

Simplify: costheta[costhetasintheta-sinthetacostheta]+sintheta[sintheta-costhetacosthetasintheta]

Simplify costheta[[costheta,sintheta],[sintheta,costheta]]+sintheta[[sintheta,-costheta],[costheta,sintheta]]

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta.[{:(sintheta,-costheta),(costheta,sintheta):}]=I.

costheta[{:(costheta,-sin theta),(sintheta,costheta):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]=?

Simplify the following : cos theta [{:(costheta,-sintheta ),(sintheta,costheta ):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

(1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

If cos theta-4sintheta=1, the sintheta+4costheta=

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 [[costheta ,-sintheta ],[sintheta ,costheta]]or[[costheta ,sintheta],[ sintheta,-costheta]]dot