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

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

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

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

If A=[[cos 2 theta, sin 2 theta],[-sin2theta, cos2theta]] , find A^2

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot 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)]

Prove that: sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta

([cos theta+i sin theta)/(sin theta+i cos theta))^(4)=?

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

Prove that (cos^3theta+sin^3 theta)/(cos theta+sin theta)+(cos^3 theta-sin^3 theta)/(cos theta-sin theta)=2