If `f(x) = [(cos theta, - sin theta, 0),(sin x, cos x , 0),(0,0,1)]`, show that `F(x) F(y) = F(x + y)`.

x = a cos theta, y = b sin theta .

If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] , show that F(x) F(y)=F(x+y) .

If A= [[cos x,sin x,0],[-sin x,cos x,0],[0,0,1]]=f(x) then A^-1=

If the matrix [[cos theta,sin theta,0],[sin theta,cos theta,0],[0,0,1]] is singular then theta=

If x = a(cos theta + theta sin theta), y = a (sin theta - theta cos theta), (dy)/(dx) =

If A= [[cos x, sin x],[-sin x, cos x]] and A(adj A)=k[[1,0],[0,1]] then the value of k is

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

The centroid of a triangle formed by the points (0, 0), (cos theta, sin theta) and (sin theta, -cos theta) lies on the line y=2x . Then theta is :

x = a (cos theta + theta sin theta), y = a (sin theta - theta cos theta) . then find dy/dx