Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**Slave****Member**- Registered: 2019-01-11
- Posts: 2

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)*

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 8,930

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

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 617

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

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

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 8,930

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

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

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