An equation of the line tangent to the graph of \( y=2x-\cos x \) at the point \((0,-1)\) is

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$$ y=2x-\cos x $$

Start by taking the derivative.

$$ y'=2+\sin x $$

The slope of the tangent line at \((0,-1)\) can be found:

$$ y'\Big|_{x=0}= 2+\sin0 $$ $$ y'= 2 $$

Using the point-slope equation:

$$ y-(-1)=2(x-0) $$ $$ y=2x+2 $$