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If F(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0...

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

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To show that \( F(x)F(y) = F(x+y) \), we will perform matrix multiplication and use trigonometric identities. Let's proceed step by step. ### Step 1: Define the matrices We have: \[ F(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ ...
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