(4) `A=[[cos(theta),sin(theta)],[-sin(theta),cos(theta)]]`; prove, `A^n=[[cos(ntheta),sin(ntheta)],[sin(ntheta),cos(ntheta)]]`

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)]

if A=[{:(costheta,sin theta ),(-sin theta,costheta):}] , then show that : A^(2)=[{:(cos2theta,sin2theta),(-sin2theta,cos2theta):}]

Simplify : cos theta [[costheta,si ntheta],[-si ntheta,costheta]]+si ntheta[[si ntheta,-costheta],[costheta,si ntheta]]

If E(theta)=[[cos theta, sin theta] , [-sin theta, cos theta]] then E(alpha) E(beta)=

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is

(sin theta)/(cos(3theta))+(sin(3theta))/(cos(9theta))+(sin(9theta))/(cos(27theta))+(sin(27theta))/(cos(81theta))=

sin^(3)theta + sin theta - sin theta cos^(2)theta =

If A=[[cos theta, sin theta],[sin theta, cos theta]],B=[[cos phi, sin phi],[sin phi, cos phi]] show that AB=BA.

If cos theta + sin theta =sqrt(2) cos theta prove that cos theta -sin theta =sqrt(2) sin theta

Prove that cos^6 theta+ sin^6 theta= 1-3sin^2 theta cos^2 theta