cos theta begin{bmatrix} cos theta & sin thet | vedclass

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Question

(D) Multiply the scalar $\cos 	heta$ into the first matrix and $\sin 	heta$ into the second matrix:$\begin{bmatrix} \cos^2 	heta & \cos 	heta \sin

Vedclass · Accepted Answer

$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$

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(D) Multiply the scalar $\cos 	heta$ into the first matrix and $\sin 	heta$ into the second matrix:$\begin{bmatrix} \cos^2 	heta & \cos 	heta \sin 	heta \ - \sin 	heta \cos 	heta & \cos^2 	heta \end{bmatrix} + \begin{bmatrix} \sin^2 	heta & - \sin 	heta \cos 	heta \ \sin 	heta \cos 	heta & \sin^2 	heta \end{bmatrix}$Now,add the corresponding elements of the two matrices:$= \begin{bmatrix} \cos^2 	heta + \sin^2 	heta & \cos 	heta \sin 	heta - \sin 	heta \cos 	heta \ - \sin 	heta \cos 	heta + \cos 	heta \sin 	heta & \cos^2 	heta + \sin^2 	heta \end{bmatrix}$Using the trigonometric identity $\cos^2 	heta + \sin^2 	heta = 1$,we get:$= \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$

$\cos \theta \begin{bmatrix} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{bmatrix} + \sin \theta \begin{bmatrix} \sin \theta & - \cos \theta \\ \cos \theta & \sin \theta \end{bmatrix} = $

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