PreCalculus - Trigonometry: Trig Identities (38 of 57) Sum to Product Formula 2

In this video I will prove cosx+cosy=2cos[(x+y)/2]cos[(x-y)/2] and cosx-cosy=-2sin[(x+y)/2]sin[(x-y)/2].

[andreqwerty]

Hello sir, thank you so much for your video it has helped me memorize the process, I would just like to point out one thing Im sure you did it to see if the viewers were actually paying attention and I thank you for doing that as it makes us really think instead of just copy.

Now to the error that you placed : Its the beginning product to sum form is it not ? before attempting a new thing I always methodically do the process from memory leading up to the new thing i am Doing and while deriving the product sum formulas the cosine - cosine formula i have gotten had a -2 from the beginning and also the cos(A+B/2) & Cos(A-B/2) were already in the correct position so at the end i didnt have to divide by -2 or flip the substituted A and B values . Even though this way arrived at the correct answer two steps faster I just would like to know if you think i should stick with this way or do the traditional way you do that requires the two extra steps only to be safe? thank you for your time