Answer:
The work is in the explanation.
Step-by-step explanation:
The sine addition identity is:
.
The sine difference identity is:
.
The cosine addition identity is:
.
The cosine difference identity is:
.
We need to find a way to put some or all of these together to get:
.
So I do notice on the right hand side the and the
.
Let's start there then.
There is a plus sign in between them so let's add those together:
There are two pairs of like terms. I will gather them together so you can see it more clearly:
So this implies:
Divide both sides by 2:
By the symmetric property we can write: