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

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

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

If f (theta) = |sin theta| + |cos theta|, theta in R , then

If A = [{:("cos" theta, -"sin"theta),("sin"theta, "cos"theta):}] , then the matrix A^(-50) " when " theta = (pi)/(12) , is equal to

If cos 3theta+sin3theta+(2sin2theta-3)(sin theta-cos theta)gt0 , then theta lies in

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 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):}]

If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1 , then theta is equal to (n in Z)

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