Answer: [tex]cos(\pi-x)=-cos(x)[/tex]
Step-by-step explanation:
We need to apply the following identity:
[tex]cos(A - B) = cos A*cos B + sinA*sin B[/tex]
Then, applying this, you know that for [tex]cos(\pi-x)[/tex]:
[tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex]
We need to remember that:
[tex]cos(\pi)=-1[/tex] and [tex]sin(\pi)=0[/tex]
Therefore, we need to substitute these values into [tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex].
Then, you get:
[tex]cos(\pi-x)=(-1)*cos(x)+0*sin(x)[/tex]
[tex]cos(\pi-x)=-1cos(x)+0[/tex]
[tex]cos(\pi-x)=-cos(x)[/tex]
