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

Answer

N/a

Explanation

` F(x)=[{:(cos x,-sinx, 0),(sinx, cos x,0),(0 ,0,1):}],`
`F(y)=[{:(cosY,-sinY,0),(sinY,cosY,0),(0,0,1):}]`
`and F(x+Y)=[{:(cos(x+Y),-sin(X+y),0),(sin(X+Y),cos(X+y),0),(0,0,1):}]`
`NOw ,L.H.S=F(x).F(Y)`
`=[{:(cosx,-sinx,0),(sinx,cosx,0),(0,0,1):}][{:(cosY,-sinY,0),(sinY,CosY,0),(0,0,1):}]`
`=[{:(cosxcosY-sinxsiny" "),(sin xcos Y+cos x sin Y" "),(" "0""),(" "-sinYcosx-sinxcosy 0),(" "-sinxsiny+cos xcos y0),(" "0" "1):}]`
`=[{:(cos(x+y),-sin(x+y),0),(sin(x+y),cos(x+y),0),(0,0,1):}]`
`=F(x+y)=R.H.S .`hence proved .