Question

Complete the identity

Answer 1

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

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)`