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The matrix R(t) is defined by R(t)=[(cos...

The matrix R(t) is defined by `R(t)=[(cos t,sin t),(-sin t,cos t)]`. Show that `R(s)R(t)=R(s+t)`.

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To show that \( R(s)R(t) = R(s+t) \), we start with the definitions of the matrices involved. ### Step 1: Define the matrices The matrices \( R(s) \) and \( R(t) \) are defined as follows: \[ R(s) = \begin{pmatrix} \cos s & \sin s \\ -\sin s & \cos s ...
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