Complete the identity

Question

asked Jul 10, 2020 22.8k views

1 Answer

Ahmed Rashad · Answer 1 · 2020-07-16T01:38:41+0000

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:

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

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

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