Simplify: $\cos θ [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}] + \sin θ [\begin{matrix} \sin θ & - \cos θ \\ \cos θ & \sin θ \end{matrix}]$

Solution

$coc θ [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}] + \sin θ [\begin{matrix} \sin θ & - \cos θ \\ \cos θ & \sin θ \end{matrix}] = [\begin{matrix} \cos^{2} θ & \cos θ \sin θ \\ - \sin θ \cos θ & \cos^{2} θ \end{matrix}] + [\begin{matrix} \sin^{2} θ & - \sin θ \cos θ \\ \sin θ \cos θ & \sin^{2} θ \end{matrix}] = [\begin{matrix} \cos^{2} θ + \sin^{2} θ & \cos θ \sin θ - \sin θ \cos θ \\ - \sin θ \cos θ + \cos θ \sin θ & \cos^{2} θ + \sin^{2} θ \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] . . . . . . . . . . [∵ \cos^{2} θ + \sin^{2} θ = 1]$

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Relations And Functions

Simplify: $\cos θ [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}] + \sin θ [\begin{matrix} \sin θ & - \cos θ \\ \cos θ & \sin θ \end{matrix}]$

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Relations And Functions

Simplify: cos θ cos θ sin θ- sin θ cos θ + sin θ sin θ - cos θcos θ sin θ

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Simplify: $\cos θ [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}] + \sin θ [\begin{matrix} \sin θ & - \cos θ \\ \cos θ & \sin θ \end{matrix}]$