I want to change the following system into a system of constant coefficients.
$x_1'=(1+\cos2t)x_1+(1-2\sin2t)x_2$,
$x_2'=-(1+2\sin2t)x_1+(1-2\sin2t)x_2$
In the question itself, they have given a hint to use the transformation below to convert it into a system with constant coefficients.
$\begin{bmatrix} x_1\\ x_2 \end{bmatrix} =\begin{bmatrix} \cos t&\sin t\\ -\sin t&\cos t \end{bmatrix} \begin{bmatrix} y_1\\ y_2 \end{bmatrix}$
But I am unable to reach the final system. Can someone help me with this? I have tried to write the new equations in $y_1$ and $y_2$ by using the existing equations. Like I wrote $x_1=\cos ty_1 +\sin ty_2 $ and similarly $x_2$. I tried differentiating it. By substituting the given system, I thought it would reduce to a system with constant coefficients. But it didn't. I tried the other way around, also. I wrote $y_1$ and $y_2$ in terms of $x_1$ and $x_2$. Then tried to construct a new system. It also didn't work out.