" 6.(i) "|[cos theta,-sin theta],[sin theta,cos theta]|" (ii) "

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1

" (i) "(cos theta+sin theta)/(cos theta-sin theta)

Simplify, costheta[[cos theta, sin theta],[-sin theta, cos theta]] + sin theta [[sin theta, -cos theta],[cos theta, sin theta]]

Verify that [(cos theta, sin theta),(-sin theta, cos theta)] and [(cos theta, - sin theta),(sin theta, cos theta)] are inverse of each other.

Simplify: cos theta[[cos theta , sin theta],[-sin theta , cos theta]]+sin theta[[sin theta, -cos theta],[cos theta ,sin theta]] .

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

If A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin theta, - cos theta), (cos theta, sin theta)] , evaluate A cos theta + B sin theta .

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