Compound angles and Double angles?

They simply tell you how to rewrite sines and cosines of a number in a way that might be more useful.

You've probably seen the identities $\sin(A+B) \equiv \sin(A) \cos(B) + \cos(A) \sin(B)$ and $\cos(A + B) = \cos(A) \cos(B) - \sin(A) \sin(B)$

If you use that to rewrite sin(x+60) and cos(x+30) in those forms then it might be more obvious what to do next. In this case for the sine part you could have A as x and B as 60, and then for the cosine, A would be x and B would be 30.

Is this what you mean : sin(x)cos(30)+cos(x)sin(60)=0.5 ?
I don't understand what to do next.
Is it possible for you to show me the working out?

You haven't applied the identity correctly.

sin(x+60), on its own, is equivalent to sin(x)cos(60) + cos(x)sin(60). Do you see how the identity gets you from sin(x+30) to that?

and then cos(x+30) becomes cos(x)cos(30) - sin(x)sin(30) if you follow the angle addition formula for cosines.

I understand that part. Thanks. But what would I do next?