Question

Simplify
$cos\theta \left[\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right]+sin\theta \left[\begin{array}{cc}sin\theta & -cos\theta \\ cos\theta & sin\theta \end{array}\right]$.

Answer 1

Given, $cos\theta \left[\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right]+sin\theta \left[\begin{array}{cc}sin\theta & -cos\theta \\ cos\theta & sin\theta \end{array}\right]$.

$\cos \theta ({\cos }^2\theta +{\sin }^2\theta )+\sin \theta ({\sin }^2\theta +{\cos }^2\theta )$

$cos\theta \left(1\right)+\sin \theta \left(1\right)=\cos \theta +\sin \theta$