Mathematics, 17.02.2021 01:40 ekarlewicz3343
Show that f(x) f(y) - f(x+y), where f(x)= [cos x - sin x o] [sin x cos x o] [o o 1]
Answers: 2
![f(x)=\left[\begin{array}{ccc}cosx&-sinx&0\\sinx&cosx&0\\0&0&1\end{array}\right] ,f(y)=\left[\begin{array}{ccc}cosy&-siny&0\\siny&cosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cosxcosy-sinxsiny&-cosxsiny-sinxcosy&0\\sinxcosy+cosxsiny&-sinxsiny+cosxcosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\](/tpl/images/1123/4642/d2c05.png)
![f(x+y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\Therefore\ f(x)f(y)=f(x+y)](/tpl/images/1123/4642/e69e1.png)
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Show that f(x) f(y) - f(x+y), where f(x)= [cos x - sin x o] [sin x cos x o] [o o 1]...
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