If `F(theta)=[[cos theta,-sin theta, 0],[sin theta, cos theta, 0],[0,0,1]]`, then show that `F(theta) F (phi)= F(theta + phi)`.

If F(theta) = [(cos theta, - sin theta, 0),(sintheta, costheta, 0),(0,0,1)] and G(alpha) = [(cos alpha, 0, sin alpha),(0,1,0),(-sinalpha, 0, cos alpha)] , show that [F(theta) G(alpha)]^-1 = G ( - alpha ) F ( - theta)

Find sin 2 theta when sin theta + cos theta= 1 .

Let A = [ (cos theta, sin theta),(- sin theta, cos theta)] , then show that A ^(2) = [(cos 2 theta, sin 2 theta),( - sin 2 theta, cos 2 theta)]

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

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

Show that if A = [[cos theta, sin theta],[-sin theta, cos theta]] , then A^n = [[cos n theta, sin n theta],[-sin n theta, cos n theta]]

Find theta , 0 sin theta = 0.7071 .

Find theta , 0 cos theta = 0.9604 .

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