Mathematics Asked by Melisa Karimi on February 21, 2021

Right now I had a question about a trigonometric system of equations and I got very good ideas. However after some modifications to the system I reached another one and following those ideas I encountered with this one:

$$A cos(2xy)+Bcos(3xy)+K sin(2xy)=W$$

$$K cos(2xy)-Asin(2xy)-B sin(3xy)=F$$

I multiple first one by A and second one by K and eliminate two terms leading to:

$$(A^2+K^2)cos(2xy)+ABcos(3xy)-KBsin(3xy)=AW+KF$$

And then to this one

$$(A^2+K^2)(2cos^2(xy)-1)+AB(4cos^3(xy)-3cos(xy))-KB(3sin(xy)-4sin^3(xy))$$

Now, I need $cos(xy)$ but I don’t idea how to do cubic terms.

Thanks

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