If `A=[[cos theta ,sin theta],[-sin theta ,cos theta]]`then prove that `A^(n)=[[cos n theta, sin n theta],[-sin n theta, cos n theta]]` `n in N`

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

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

If A= [[cos theta,sin theta],[-sin theta,cos theta]], then lim _(n rarr infty )A^(n)/n is (where theta in R )

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

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

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

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

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

Prove that (cos theta+sin theta )^2 + (cos theta - sin theta )^2 =2