How to prove the sum-to-product identity for sine: sinA+sinB=2sin((A+B)/2)cos((A-B)/2)

How to prove that sinA+sinB=2sin((A+B)/2)cos((A-B)/2)

[franseresplandor]

this is probably the best teacher I have in terms of all the trigonometic identities. Very simple and consice! Love it!

[shrihari]

Sir now Ill completely forget memorizing these formula
Because from Now on I can derive these formula anytime, anywhere
Long Live BlackPenRedPen Yeeay!!!

[jaywyn]

My textbook did a terrible job explaining this proof, and most proofs I found involve proving itself. Thanks for making this proof crystal clear. Well done.

[carterwoodson]

I am so happy you put this up 2 YEARS AGO!!! thank you so much, never investigated these relationships

[humester]

5*: Everything I have found on the Internet so far has been a proof, not a derivation; meaning that they start with the answer and then simplify the answer on the RHS to equal the LHS. Yours is the first real derivation I've found. Love it!

[crystalhuang]

I have been looking for a proof just like this and found it. Thank you so much!

[reazraza]

Blackpenredpen white paper. You are uplifting the channel name. Good job!

[diesitreinta]

This proof videos are my favorite, thanks! Love u ❤

[JJ-ujwi]

Thank you! I have been find the proofs for this, since the precalculus lesson I attended didn't prove this for us

[gustavosedano]

That demostrative videos are amazing!!!

[julianarodrigues]

You make me so happy now, thanks a lot!

[BigDBrian]

an informal way to derive alpha in terms of A and B:
Say for example we take sin(40) + sin(60). how would we determine alpha and beta? well, it's not too hard to see it'll be 50-10 and 50+10. alpha is fifty, because it's the average, and beta is 10, because its the difference between each term and the average.

[headmanlesetlhe]

beautiful magnificently explained.... thank you so much

[sansamman]

THIS IS SO FUN! please keep on proving stuff and do more videos with this OG style!!

[marcioamaral]

Pretty easy identity to prove but still a useful one

[jagsingh]

Thank you very much!!! It becomes so much easier to memorise now that I know how it works, video very much appreciated!

[rithiek]

Wanted to say Thank you! Learnt a lot from you till date :)

[eleazaralmazan]

Can you make videos explaining how to solve equations involving the floor function? An example of such equation would be floor(x)-2floor(x/2) = 1.
Great videos by the way!

[gergodenes]

For the difference, it is
I love these so much. All just connects together. I lvoe math.

[tasninnewaz]

Everybody know this. your are my favourite teacher and i hoped that it will be a geometric explain.