Evaluate-
`|[costheta,sintheta],[sintheta,costheta]|`

Evaluate costheta/(1+sintheta)

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

Choose the correct answer from the following : The value of |{:(-costheta,sintheta),(-sintheta,-costheta):}| is:

Evaluate [(1+costheta)/sintheta]^2

costheta[[costheta, sintheta], [-sintheta, costheta]]+sintheta[[sintheta, -costheta], [costheta, sintheta]]=

Evaluate costheta.costheta+sintheta.sintheta

Evaluate costheta/sintheta

Evaluate the determinants in |{:(costheta,-sintheta),(sintheta,costheta):}|

If A=[[costheta, sintheta], [-sintheta, costheta]] , then

Show that every real orthogonal matrix is of any one of the forms {:[(costheta,-sintheta),(sintheta,costheta)]:}or{:[(costheta,sintheta),(sintheta,-costheta)]:}