If cos(x-10) = sin(4x), a value of x is

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Chartwig4831

02.09.2022

Mathematics

A slightly different method: Using the polynomial remainder theorem, you have

$x^3+px^2+qx+6\bigg|_{x=-1}=-1+p-q+6=0\implies p-q=-5$
$x^3+px^2+qx+6\bigg|_{x=2}=8+4p+2q+6=0\implies 2p+q=-7$

Adding these equations together, you get

$(2p+q)+(p-q)=-12\implies 3p=-12\implies p=-4$
$p-q=-5\implies -4-q=-5\implies q=1$

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