If R(t) = begin{bmatrix} cos t & sin t -sin | vedclass

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(C) Given $R(t) = \begin{bmatrix} \cos t & \sin t \ -\sin t & \cos t \end{bmatrix}$.Then $R(s) = \begin{bmatrix} \cos s & \sin s \ -\sin s & \cos s

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$R(s + t)$

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(C) Given $R(t) = \begin{bmatrix} \cos t & \sin t \ -\sin t & \cos t \end{bmatrix}$.Then $R(s) = \begin{bmatrix} \cos s & \sin s \ -\sin s & \cos s \end{bmatrix}$.Calculating the product $R(s) \cdot R(t)$:$R(s) \cdot R(t) = \begin{bmatrix} \cos s & \sin s \ -\sin s & \cos s \end{bmatrix} \begin{bmatrix} \cos t & \sin t \ -\sin t & \cos t \end{bmatrix}$$= \begin{bmatrix} \cos s \cos t - \sin s \sin t & \cos s \sin t + \sin s \cos t \ -\sin s \cos t - \cos s \sin t & -\sin s \sin t + \cos s \cos t \end{bmatrix}$Using trigonometric identities $\cos(A+B) = \cos A \cos B - \sin A \sin B$ and $\sin(A+B) = \sin A \cos B + \cos A \sin B$:$= \begin{bmatrix} \cos(s+t) & \sin(s+t) \ -\sin(s+t) & \cos(s+t) \end{bmatrix}$$= R(s+t)$.

If $R(t) = \begin{bmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{bmatrix}$,then $R(s) \cdot R(t) = $

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