(cosec `theta` -sin `theta`) (sec `theta` - cos `theta`) (tan `theta` + cot `theta`) = 1.

Prove the following identity : (sec theta-cos theta) (cosec theta-sin theta)=1/(tan theta+ cot 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 .

Prove that : (sec theta-tan theta)/(sec theta+tan theta)= 1-2 sec theta tan theta+ 2 tan^2 theta .

Prove that (sin theta- "cosec" theta )(cos theta- sec theta )=(1)/(tan theta + cot theta).

Prove that (1 +cot theta -cosec theta )(1+tan theta +sec theta )=2.

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec 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.

Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+ cosec theta)^2= (1+ sec theta cosec theta)^2 .

Prove that cot theta cot 2 theta+ cot 2 theta cot 3 theta+ 2= cot theta (cot theta- cot 3 theta) .