Question

HELP PLEASE 30 POINTS! WILL MARK BRAINLIEST IF CORRECT!!!!!

Answer 1

Answer:

this is a required answer.

Answer 2

Answer:

See Below.

Step-by-step explanation:

We want to verify:

$\cos(x-y)-\cos(x+y)=2\sin(x)\sin(y)$

We will utilize the following identities:

$\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)$

And:

$\cos(x+y)=\cos(x)\cos(y)-\sin(x)\sin(y)$

So, by substitution, we acquire:

$(\cos(x)\cos(y)+\sin(x)\sin(y))-(\cos(x)\cos(y)-\sin(x)\sin(y))=2\sin(x)\sin(y)$

Distribute:

$\cos(x)\cos(y)+\sin(x)\sin(y)-\cos(x)\cos(y)+\sin(x)\sin(y)=2\sin(x)\sin(y)$

The first and third term will cancel:

$\sin(x)\sin(y)+\sin(x)\sin(y)=2\sin(x)\sin(y)$

Combine like terms:

$2\sin(x)\sin(y)\stackrel{\checkmark}{=}2\sin(x)\sin(y)$