Math Is Fun Forum

Slave

Member

Registered: 2019-01-11

Posts: 2

sin(A+B) sin(A-B) derivation

Hello,
I am having trouble understanding the steps of deriving the above mentioned functions. I know how to get their value and also how to derive their value from sine and cosine. But what I want to know is that how did they derive it first time ? How would they think of drawing such a figure ? I would be grateful if you guys provide me with the train of thought which led to the figures and eventually the derivations.

Last edited by Slave (2020-06-21 18:19:51)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: sin(A+B) sin(A-B) derivation

hi Slave

I'm not quite sure what you're after here, but maybe it's this:

So let A+B = P and A-B = Q

Substitute in the above (I've swapped the LHS with the RHS)

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

666 bro

Member

From: Flatland

Registered: 2019-04-26

Posts: 706

Re: sin(A+B) sin(A-B) derivation

I think he asked about how trigonometric angle identities got derived and where did it came ?

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"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: sin(A+B) sin(A-B) derivation

hi 666bro,

I did wonder that as I posted.  I hoped he'd come back if I hadn't given what he wanted.

There's a proof of the compound angle formulas here:

http://www.mathisfunforum.com/viewtopic … 28#p389628

There is also a proof using Euclidean geometry (strictly only works for angles under 90).  Not sure if it's ever been posted … I think maybe it has.  If not I'll do it if somebody asks.

edit: found it

http://www.mathisfunforum.com/viewtopic … 88#p410288

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob