The title of the question is: Using graphical technique determine the single wave resulting from a combination of two waves of the same frequency and then verify the result using trigonometrical formula
Already done part a, I'm on part b now, I have no idea what to do. If you can't read anything on the picture I can clarify it for you.
Use the sum-difference formula for $\sin$:
$$\sin(\alpha \pm \beta) = \sin\alpha \cos\beta \pm \cos \alpha \sin \beta$$
Use the sum ($+$) when two angles are being added, and difference $(-)$ when two angles are being subtracted.
Added: For your equations, you might also like to know that you can distribute the scalar A. E.g.
$$v_1 = \;A\sin(\omega t + \phi_1) = A(\sin\omega t \cos\phi_1 + \cos \omega t \sin \phi_1) = A\sin\omega t \cos\phi_1 + A \cos \omega t \sin \phi_1$$