I'm having trouble with Sum and Difference identity problems like one in the photo and I am unsure of how to go about solving it.

[Bluebobber]

I can solve problems that covers one graph but I don't know what to do when there is two of them.

 

[Dr.Peterson]

View attachment 37448
I can solve problems that covers one graph but I don't know what to do when there is two of them.

Use the graphs one at a time to determine [imath]\sin(\alpha)[/imath] and [imath]\cos(\alpha)[/imath], and [imath]\sin(\beta)[/imath] and [imath]\cos(\beta)[/imath].

Then apply the identity.