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MrPolygon
![A=\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]\\\\{}\\A^2=AA=\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]\cdot\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]=\\\\=\left[\begin{array}{cc}\sin^2x+\cos^2x&\sin{}x\cos{}x+\cos{}x\sin{}x\\\cos{}x\sin{}x+\sin{}x\cos{}x&\cos^2x+\sin^2x\end{array}\right]=\\\\=\left[\begin{array}{cc}1&\sin2x\\\sin2x&1\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Csin%7B%7Dx%26%5Ccos%7B%7Dx%5C%5C%5Ccos%7B%7Dx%26%5Csin%7B%7Dx%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7B%7D%5C%5CA%5E2%3DAA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Csin%7B%7Dx%26%5Ccos%7B%7Dx%5C%5C%5Ccos%7B%7Dx%26%5Csin%7B%7Dx%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Csin%7B%7Dx%26%5Ccos%7B%7Dx%5C%5C%5Ccos%7B%7Dx%26%5Csin%7B%7Dx%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Csin%5E2x%2B%5Ccos%5E2x%26%5Csin%7B%7Dx%5Ccos%7B%7Dx%2B%5Ccos%7B%7Dx%5Csin%7B%7Dx%5C%5C%5Ccos%7B%7Dx%5Csin%7B%7Dx%2B%5Csin%7B%7Dx%5Ccos%7B%7Dx%26%5Ccos%5E2x%2B%5Csin%5E2x%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26%5Csin2x%5C%5C%5Csin2x%261%5Cend%7Barray%7D%5Cright%5D "A=\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]\\\\{}\\A^2=AA=\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]\cdot\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]=\\\\=\left[\begin{array}{cc}\sin^2x+\cos^2x&\sin{}x\cos{}x+\cos{}x\sin{}x\\\cos{}x\sin{}x+\sin{}x\cos{}x&\cos^2x+\sin^2x\end{array}\right]=\\\\=\left[\begin{array}{cc}1&\sin2x\\\sin2x&1\end{array}\right]")
![A^3=A^2A=\left[\begin{array}{cc}1&\sin2x\\\sin2x&1\end{array}\right]\cdot\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]=\\\\=\left[\begin{array}{cc}\sin{}x+\cos{}x\sin2x&\cos{}x+\sin{}x\sin2x\\\cos{}x+\sin{}x\sin2x&\sin{}x+\cos{}x\sin2x\end{array}\right]](https://tex.z-dn.net/?f=A%5E3%3DA%5E2A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26%5Csin2x%5C%5C%5Csin2x%261%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Csin%7B%7Dx%26%5Ccos%7B%7Dx%5C%5C%5Ccos%7B%7Dx%26%5Csin%7B%7Dx%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Csin%7B%7Dx%2B%5Ccos%7B%7Dx%5Csin2x%26%5Ccos%7B%7Dx%2B%5Csin%7B%7Dx%5Csin2x%5C%5C%5Ccos%7B%7Dx%2B%5Csin%7B%7Dx%5Csin2x%26%5Csin%7B%7Dx%2B%5Ccos%7B%7Dx%5Csin2x%5Cend%7Barray%7D%5Cright%5D "A^3=A^2A=\left[\begin{array}{cc}1&\sin2x\\\sin2x&1\end{array}\right]\cdot\left[\begin{array}{cc}\sin{}x&\cos{}x\\\cos{}x&\sin{}x\end{array}\right]=\\\\=\left[\begin{array}{cc}\sin{}x+\cos{}x\sin2x&\cos{}x+\sin{}x\sin2x\\\cos{}x+\sin{}x\sin2x&\sin{}x+\cos{}x\sin2x\end{array}\right]")
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