The students in that class were so fortunate to have Eddie Woo as their teacher. This guy is something else, after just 7 mins I have solved my first Trig identity proof.
@AliMohamed-qu9qm8 ай бұрын
whomp whomp
@jupitahrАй бұрын
@@AliMohamed-qu9qm first of all it's spelled womp womp, second what are they complaining about to even womp womp at?
@eleliminador40103 жыл бұрын
To be honest, this man is the coolest teacher i have seen in my whole life, youre the best eddie
@potatochips90194 жыл бұрын
I wrote the incorrect steps in the exam and got marked wrong for it. I asked my teacher why and she don't give me a reason for it. I had argued with her in front of the class for half the lesson and still don't get why. And here Mr Woo just explains it in literally 2 mins. I thank you so so much for the explanation!
@reubenmanzo20542 жыл бұрын
In short, you're using the statement that you've been asked to prove to prove the statement, and since that relies on the statement being true in the first place, it's a logical fallacy known as circular reasoning.
@amateurtries7542 Жыл бұрын
Is it possible that she herself didn't know it, and just marked it wrong because that wasn't how the textbook showed the proof?
@user-sk3nf2vv4p9 ай бұрын
in short i dont understanad a single word on your sentences@@reubenmanzo2054
@MrMr02483 жыл бұрын
Imagine actually having a maths 'Teacher'
@evielily73502 жыл бұрын
Maths' lol brits
@NoWarInBaSingSe2 жыл бұрын
Ha ha!
@Amitsa2996 жыл бұрын
I was feeling sleepy than I switch to your video and all sleep gone, thank you to you and your energy level.
@user-ki6pt2zg1h3 жыл бұрын
Watch this video examination in life never give up-kzbin.info/www/bejne/oWXaZaOXoJtpjJI
@shafzkay15945 жыл бұрын
DAMN ur acc so sick. u literally blew my mind with the explanation at the very end
@mathematechxblackboard19423 жыл бұрын
Perfect! I have seen this a lot from my students who go to my class with prior knowledge in trigonometry and they present their proofs by starting with the "equation" instead of working from one side to reach the other.
@ryiv18482 жыл бұрын
This is exactly how I prove trig. identities even before watching this video. I make an end for both sides through simplification and manipulating identities then makes those ends meet. I learned a lot through this video resurfacing my knowledge about proving trig. identities
@Drforeverok Жыл бұрын
Best math teacher ever. Literally never seen a better youtuber who teaches math. Thanks so much
@ferdousibegum1317 Жыл бұрын
U are a total lifesaver......gosh how can anyone explain math like that?????
@iglo12094 жыл бұрын
I wish this guy was my math teacher. like the energy and hand gestures and the way how you simplify your explanations so its so easy to understand.... Man thank you so much. Its my first time watching your video and I was hella sleepy, but I felt like I was in the actual classroom when I was watching this video.
@evan.59674 жыл бұрын
이원원 Everyone wishes that uWu
@morgard2114 жыл бұрын
There is a simillar problem with prove by induction. By plugging in n + 1 into a formula and ending with 0 = 0, you just prove that zero is equal to zero. Exactly as you say, you need to end with n + 1 equivallent of the original formula.
@justshan24133 жыл бұрын
I loved your approach on how to solve complicated Trigonometric Identities.
@rofahad98733 жыл бұрын
Me too! I wouldve never thought of that
@aadityachavan7813 жыл бұрын
That is exactly how we are taught using LHS=RHS atleast here in India I don't about USA
@kumarkartikerollno2094 Жыл бұрын
These were complicated 😂
@RedFrost64 ай бұрын
yeaa@@aadityachavan781
@DarinBrownSJDCMath4 жыл бұрын
If each equation is known to be equivalent to the previous one (i.e. you have a string of if and only if's) then there is nothing "wrong" with the first "incorrect" proof you gave. You are simply showing that Equation 1 Equation 2 Equation 3 and since you know Equation 3 is an identity, the first equation must also be an identity. It's a perfectly correct approach to take, provided you understand the reasoning involved. You're not "assuming what you're trying to prove." You're proving that the identity you want to prove is equivalent to a known identity. What you CAN'T do is start with an equation you want to prove is an identity, prove that this equation implies an identity, and then say you've proved the original equation is an identity. For example, you can't start with -3 = 3, square both sides, and say since 9 = 9, we know that -3 = 3 is an identity. That's because the implication only runs in one direction. I would also say it's incorrect to say that an identity is NOT an equation. An identity is simply an equation that is true for all values of the variables under consideration.
@TheHuesSciTech4 жыл бұрын
I'd say this: all you have to do is rewrite all the same formulas in reverse order (starting from the identity cos^2 theta = cos^2 theta, and ending with the thing you're trying to prove.) You ALSO need to check that each logical step is still valid (no multiplications by zeros, or multiplications by *anything* not known to definitely be nonzero), and you're left with a rigorous proof.
@folalibi27433 жыл бұрын
I agree with you, Darin. The danger of solving an equality as if it were an equation (as in the example Eddie marks as "incorrect") is that some students will inevitably get tempted to switch terms between the left- and the right-hand side. In the example given, that would mean moving the cos^2 to the left and the -1 to the right to obtain the known Pythagorean identity, and then concluding that the original identity was true because the Pythagorean identity is true. And that would not be a proof.
@fardinkhanmahi84933 жыл бұрын
@@TheHuesSciTech 义乌市我坏死🈚也额度文件夹啊就是一丢丢绝对可靠地低俗还是UE里
@jamiewalker3293 жыл бұрын
@@folalibi2743 Yes it would be if there were if and only if arrows...
@kianwoolston16733 жыл бұрын
I’m in year 9 and I don’t know what any of these symbols means but he just made it so understandable that it seems easy. Great video
@preciousbees57213 жыл бұрын
2:28 - 55 “I started with this, I can’t start with this I’m supposed to end with this so that can’t be the first line that’s gotta be the last line I’ve got it completely backwards. You’re meant to prove this the burden of proof is in you it’s like walking into a legal court and you’re the defense well everyone assuming THAT my client is innocent... you can’t use that as your basis”
@RedFrost64 ай бұрын
I wish we had a teacher like you lol
@theflaminglionhotlionfox21403 жыл бұрын
God I love your accent so much
@MunnaBhai073 ай бұрын
Damn man u r too good
@wackeydelly20162 жыл бұрын
If it says verify the first option he showed is valid. Since it says "prove" you cannot use what you started with in your proof. Usually these type of questions are written a little different to avoid this issue like "given (1-sinx) and (1+sinx), prove that their product is equal to cos^2(x). Then you dont even need LHS and RHS. Just do the distributive property, use the identity and end proof.
@lukasmoudry99732 жыл бұрын
Except the part when he says you can't do that, which you absolutely can and it is right and there is nothing wrong about it, nice video
@user-or7cm1vc1y4 ай бұрын
Glad I'm not the only one that thought it was totally absurd to say that you can't do this. I love this guy but he's dead wrong here
@jasonappel5486Ай бұрын
This is such a good guide. My actual math teacher made me want to jump in front of a train instead of doing the finals.
@constantinknab7 ай бұрын
this lecture is amazing!
@AceOfHearts0013 жыл бұрын
Brilliant!!
@tsgojas31812 ай бұрын
Very fortunate students
@bhartikirdat19146 жыл бұрын
you are the best
@Liam-ve1ir3 жыл бұрын
Eddie Woo has to be one of the best teachers of on this planet
@uselesslynishat3 жыл бұрын
I wish my teachers whiteboard was that big because they always rub thing out for space
@adam98413 жыл бұрын
dude, ur a legend. readers, if u think his explanation did not make sense, then go make ur own vid. peace
@josda10006 жыл бұрын
Eddie Woo, the description of this video seems to have been hacked...
@kennethwong78395 жыл бұрын
Its not hijacked, the topic is actually proving whether these identities are equal on both sides. The topic you are referring to should be proving trignometric functions
@James-le8gd5 жыл бұрын
There is a trojan horse in the description
@insteadnotschoolthaninvain9957 Жыл бұрын
I need more theory
@zac9212910 ай бұрын
I still don't understand why you can't just start with the identity. If you start with the identity, and then compute the equation (via algebraic manipulation/known theorems) until you reach 0=0, you've effectively proven that the identity is just as true as 0=0. Since 0=0 is clearly true, then so is the identity, and I believe that you have provided sufficient proof. If you were to do this with something that wasn't actually an identity, your final line of working would not reach something that wasn't unequivocally true (i.e. you wouldn't be able to get to 0=0). Therefore this line of working is something that's non-replicable with non-identites, and we can accept it as proof for the given identity. Can someone please help me understand what is wrong with this line of thinking? Thank you.
@darcylim60373 жыл бұрын
after proving an identity i add 'therefore proven' just to gain that extra satisfaction.
@bonzolo23582 жыл бұрын
W teacher and class
@glydelsolis5066 Жыл бұрын
I would love math if he's my instructor T_T
@kumarkartikerollno2094 Жыл бұрын
I am in class 9th , and I am solving these identities since 8th grade and I came here to learn to solve quickly 😅 , but this was just the intro 😆lol
@ayushkumarnayak9576 Жыл бұрын
🤣
@sira88672 жыл бұрын
I have a question can we expand the brackets and then use the trigonomtry identies?
@jashenjunais62916 ай бұрын
harder questions please
@kasomamwansa16116 жыл бұрын
i love this topic
@jamiewalker3293 жыл бұрын
But there is literally nothing wrong with the first method. Just use bivariate implication arrows. Also if LHS = sin^2 (t) and RHS = sin^2 (t) then LHS = RHS by transitivity of equality - no need to write ANYTHING in reverse. . There is absolutely NO NEED to manipulate the LHS into the RHS or vice versa - I wish teachers would stop claiming this as it stifles creativity when constructing proofs. A proof by contradiction also works. Let's assume that there exists a value of t such that the inequality doesn't hold - then you can then argue from that, that cos^2 (t) doesn't equal cos^2 (t).
@alguem244 күн бұрын
I think youtube is wrong, 2015 isn't 9 years ago. Right? Right??
@lleiann4 жыл бұрын
OMG I UNDERSTAND SOMETHING THANK YOU
@evan.59674 жыл бұрын
Leian Abundo Wow, great to hear! But why the caps?
@tastypencil4 жыл бұрын
why do you need to go in reverse at the end if a=b and c=b cant u just say a=c
@tastypencil4 жыл бұрын
@Aakash Mandava bruh how is it a fallacious argument if 1+1 = 2 and 3 - 1 = 2 1 + 1 = 3 - 1 what is wrong here?
@aakashm99624 жыл бұрын
@@tastypencil But what you're saying isn't actually the exact same thing. It's right, but when we're trying to prove an identity like, say, a = c, we can't assume that a = c is true. In other words, if we had to prove it, our steps shouldn't start with a = c, because that's exactly what we have to prove. So what you have to do is take LHS, a, the do some nifty maths, and make sure you end up with c. So, taking your example of: Prove: a = c a = b c = b Hence, a = c. Sure, it's mathematically correct. But where did you get c from? The questions is asking you to arrive at c from a. Not take both a and c, and arrive at the same thing, b. Your first step a = b is correct. But you have to work in reverse to take b and end up with c. Basically, you must end at c to successfully prove the identity. Bit of a long answer but I hope that helps.
@tastypencil4 жыл бұрын
@@aakashm9962 i mean ye but commutative law? if it asks to prove a = c and u start with c and prove it equals a, youve proved c=a, which is the same as a=c The only thing you've assumed is that c exists. I get what you're saying tho, it appears to be just a convention of proofs that you have to start from the side it says and then end on the RHS. Seems dumb tho, i mean when you're literally reversing your working out Thx for the clarification!
@DarinBrownSJDCMath4 жыл бұрын
@Aakash Mandava It makes no sense to say the "RHS is true". The RHS is an expression, not an equation. If you want to prove a = c is an identity, it's perfectly okay to prove a = b and c = b are identities and then combine them.
@DarinBrownSJDCMath4 жыл бұрын
@@aakashm9962 It's not assuming what you're trying to prove. You're taking known identities and combining them to get a new identity.
@somtimesieat24113 жыл бұрын
Woo Wednesday hours
@SubhashKhakre3 ай бұрын
He explained easy thing complicatedly...
@SaharaDusted6 ай бұрын
5:06
@sayushamatya83303 жыл бұрын
Proof by contradiction!?
@shakjo70454 жыл бұрын
I want video to how to get fake subscribers 101
@elliotskunk Жыл бұрын
that was insanely useful
@masterjiraiya24103 жыл бұрын
It's the basic trigonometry taught to every Asians
@RaffaelloLorenzusSayde3 жыл бұрын
How to prove the the following identity 'sin8x=8sinxcosxcos2xcos4x' step by step.. I've been stuck on this one for 3 hours. Any help would be great thanks 😊
@mrrealnobody43823 жыл бұрын
Do u still need it?
@RaffaelloLorenzusSayde3 жыл бұрын
@@mrrealnobody4382 not anymore, that was a while back but thanks
@benhbr5 ай бұрын
Or simplify LHS - RHS to 0
@rossphillipgerard3 жыл бұрын
When anyone shows me how not to do something I get mad
@eleliminador40103 жыл бұрын
Chill
@rossphillipgerard3 жыл бұрын
@@eleliminador4010 That doesn't work. Sometimes somebody yells, sit boy sit. I don't sit either
@amvrabbit Жыл бұрын
i remember my teacher teaching us thins in high school 1st year.... but this guys teaching skills are way better than him
@mina865 жыл бұрын
That's rather silly. In the first example, all steps use logical equality so it's a perfectly fine proof. In the last example, just finish up with LHS = sin²θ = RHS. There's no need to waste time writing stuff in reverse.
@larsk19245 жыл бұрын
He just wrote down the exact same stuff as in the first example. Also, whenever you have to proof something is true there is no wrong in assuming the point is true; Whenever the point to proof is 'false', you will eventually encounter a statement like 1=2. I don't seem to get what's wrong with the first ex.
@rusejames72424 жыл бұрын
Exactly, they are all biconditional statements
@XxStuart96xX4 жыл бұрын
You are asked to prove that LHS = RHS though. To do that you need to show that starting at the LHS, you can end up at the RHS. Notice the first example have the same steps both times. But writing '= cos^2(x)' each time is bad in the sense that that is what you are wanting to end up with. Instead of proving that LHS = RHS, you are assuming LHS = RHS and then verifying it, which is not the same. Again with the second example, you are wanting to start from the LHS and after multiple steps, finish with the RHS. It may sound pedantic, but by just saying LHS = sin^2(x) = RHS, you have not shown the steps to get from sin^2(x) to RHS, so you have not yet shown how to get from the LHS to the RHS.
@rusejames72424 жыл бұрын
@@XxStuart96xX if you assume an identity is true and could manipulate it through biconditional operations to a true statement that means the original identity must be true. High school teachers may not like it, but that's totally valid in formal logic. If it were false there would be a contradiction, resulting in a false statement.
@tastypencil4 жыл бұрын
@@rusejames7242 "Ruse James" ahhaha
@phillipsmith18474 жыл бұрын
So tell me why 1-sin^2 theta =cos^2 theta. Otherwise, it's just a(n) (il) logical mathematical syllogism that has no meaning or purpose. So what is its purpose? How can this used in real life situations to solve real world problems? If it can't, I don't see the point of it.
@Jayantea Жыл бұрын
I was doing it the wrong way, thanks
@KrishnaGupta620783 жыл бұрын
I am from India 🇮🇳🇮🇳🇮🇳🇮🇳 to see your video
@d9xv9062 жыл бұрын
WTF?!?!?!
@dsa26853 жыл бұрын
Wtf is wrong with you. It's an if not an is. It doesn't say that it's outright true but we're going within the constraints of mathematics to check if it's true.
@prashantdubey94304 жыл бұрын
u know the feeling when u r trying to make it too easy for the students and then we just mess up the whole class....so the same thing written on top is wrong but on bottom is right..da hell is ur point ..
@adellehussein92135 жыл бұрын
You need to be more quiet and slow to get informed from your big knowledge thxs