Show that the matrix `[{:( cos theta , sin theta ),(-sin theta , cos theta ):}]` is orthogonal

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

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

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

Find the characteristic roots of the two-rowed orthogonal matrix [(cos theta,-sin theta),(sin theta,cos theta)] and verify that they are of unit modulus.

Solve sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta .

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

Find the distance between the points : (cos theta, sin theta), (sin theta, cos theta)

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

If cos2theta=0 , then |(0,costheta,sin theta),(cos theta, sin theta, 0),(sin theta, 0, cos theta)|^(2) is equal to…………

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.