If `f{x}=[{:(cos x,-sinx,0),(sin x,cos x,0),(" "0," "0,1):}]`, then which of the following are correct ?
1. `f(theta) xx f(phi)=f(theta + phi)`
2. The value of the determinant of the matrix `f(theta) xx f(phi)` is 1.
3. The determinant of f(x) is an even function.

If f(x)=[{:(cos x, -sin x, 0),(sin x, cos x, 0),(0,0,1):}] , then which of the following are correct ? 1. f(theta) xx f(phi) = f(theta +phi) . 2. The value of the determinant of the matrix f(theta) xx f(phi) is I. 3. The determinant of f(x) is an even number Select the correct answer using the codes given below :

If f(x) = [(cos x , - sinx,0),(sinx,cosx,0),(0,0,1)] then show f(x) . f(y) = f(x+y)

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Given that F(x)=[{:(,cos x,-sin x,0),(,sin x,cos x,0),(,0,0,1):}]."If"in R Then for what values of y, F(x+y)=F(x)F(y)

If f(theta)=[(cos theta, -sin theta,0),(sin theta, cos theta, 0),(0,0,1)] then {f(theta)^(-1)} is equal to

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

If sin theta sin phi - cos theta cos phi+1 =0 then the value of 1+ cot theta tan phi is-