An Incredibly ¬Important Trigonometric Identity!

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Yes, we are going to do the impossible. Let us derive an addition theorem for the difference of tangent arguments, namely tan(a+b) and tan(a-b). Enjoy the sht :vvvvvvvvvvv

[harrygreen]

Swole mathematical arms from writing out all the theorems

[quantum]

Me before watching: Oh trig identities. Finally a video I can understand

Me 15 seconds in: wat?

[sionae]

You were so close to the 10 minutes... press f for our papa flammy

[thelightningwave]

You were 15 seconds away from breaking your word. Lol

[youurdream]

When drawing triangles is too difficult so you need to "complexify" your life xD

[tomasblovsky]

1:51 ... I was looking at your "Im" .. I thought it was ln and I was like what the hell :DDD I loved that you used complex analysis here, it makes everything easy, especially with this goniometric stuff. Also loved the negation sign in front of the word "Important" in the name of the video :DDD

[zh]

I had to memorise those addition formulae at school. I never understood where they came from. Now I see that if you express them all as complex exponentials it's all quite simple! We weren't allowed to know that at the time because i doesn't get officially introduced until your last year at school...:-(

[carlosp]

I remember doing this when I was getting my pHd in theoretical engineering

[josephchaaban]

This is entertainment in its purest form. <3

[garvett]

The “not” sign in the title is such a subtle joke.

[pythagorasaurusrex]

Hello Flammy, well done explanation of deriving that formula with complex numbers. But.... I wonder why you made a video about it when someone needs an advanced level of understanding math. You will have had your reason so no complain about that.
I would have done it by just using real numbers, the addition theorem of sin and cos and simply using the definition of the tan=sin/cos.

So here we go:

Now I am expanding the whole fraction with

that gives me a double fraction which looks brutal at first glance, but terms simplify nicely to .. by just using the definition of tan and cancelling all remaining cos(x) and cos(y).

[gagers]

This keeps appearing in random physics questions involving friction and people keep ignoring this huge simplification of writing stuff in terms of tan smh.

[cobalt]

Why go into all of the complex analysis at the beginning instead of just expanding the angle additions of sine and cosine?

[MrRyanroberson]

Pappa flammy: so sexy his sleeves burned off

[psilvakimo]

Let's hear it for de Moivre's Theorem!

[Monarcha_Mortis]

Papa showing his muscles to za warudo for 9mins

[luchisevera]

Math doctor Bob is smiling approvingly in the distance

[lukamitrovic]

Tfw he could have used pure algebra but papa OILEr

[knochiosiedlerfreund]

Na, so wie Du mit Deinen Armen herumfuchtelst (was ich nicht böse meine), erinnerst Du mich ein wenig an Kermit den Frosch. Schön, dass es Dir aber wieder bissl besser zu gehen scheint, trotz des kratzenden Halses. Was auch immer sich bei Dir getan zu haben scheint, mach weiter so. Das ist wieder ein Video, bei dem Du frisch und vital wirkst und dank Muskelshirt auch ziemlich sexy. ;)

Inhaltlich konnte ich Deinem Video prima folgen, bei den vergangenen Videos von Dir kam ich intellektuell nicht mehr ganz hinterher, ist bei mir auch schon eine gefühlte Ewigkeit her, dass ich mich damit befassen musste.

Ich hoffe, Deinen Geburtstag hast Du ordentlich feiern können, 18 Jahre wird man ja auch nur einmal ;)

Auf jedenfall bedanke ich mich dafür, dass Du mir dabei hilfst mit Deinen Videos, verloren geglaubtes Wissen bei mir wieder aufzufrischen. Ich freue mich schon auf die nächsten Videos, denen ich hoffentlich ebenso gut folgen kann, wie dieses hier.

Liebe Grüsse

Ralf

[ListentoGallegos]

minor question. Why does the equation have the equivalence, "three bars", symbol and not the equals sign? Is it just a stylistic choice conveying that both sides are equal?