Question

Complete the identity

Answer 1

Answer: $cos(\pi-x)=-cos(x)$

Step-by-step explanation:

We need to apply the following identity:

$cos(A - B) = cos A*cos B + sinA*sin B$

Then, applying this, you know that for $cos(\pi-x)$:

$cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)$

We need to remember that:

$cos(\pi)=-1$ and $sin(\pi)=0$

Therefore, we need to substitute these values into $cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)$.

Then, you get:

$cos(\pi-x)=(-1)*cos(x)+0*sin(x)$

$cos(\pi-x)=-1cos(x)+0$

$cos(\pi-x)=-cos(x)$