In this case, we will use the sum formula for the cosine to write an equivalent expression. Given angles a and b we have that
[tex]\cos (a+b)=\cos (a)\cos (b)\text{ - sin(a)sin(b)}[/tex]
In our case , we have that a=pi, b=x. So
[tex]\cos (\pi+x)=\cos (\pi)\cos (x)\text{ -sin(pi)sin(x)}[/tex]
Recall that
[tex]\cos (\pi)=\text{ -1}[/tex]
and
[tex]\sin (\pi)=0[/tex]
so we have that
[tex]\cos (\pi+x)=\text{ -1}\cdot\cos (x)\text{ - 0}\cdot\sin (x)=\text{ -cos(x)}[/tex]
