In Russia, similar trigonometric equations are part of the state exam

@shortsornothing4981

Жыл бұрын

In India too

@UPSC_Juction_

Жыл бұрын

@@shortsornothing4981 Board

@panchanansahoo6559

Жыл бұрын

Very good

@ovsyanka39

Жыл бұрын

Это неправда

@vigneshb2790

Жыл бұрын

Russia is the only friendly country for india

I always forget about u subs outside of integrals for some reason. What a straightforward way to solve such a seemingly difficult problem!

Nicely explained.

Let t=81^{sin^2(x)}, then 81^{ cos^2(x)}= 81^{ 1- sin^2(x)}=81/t and original equation will become t +81/t = 30. This is a quadratic equation and very easy to solve.

@miketaya8128

Жыл бұрын

No the answer is 7 shut up

@dhruvjha2776

Жыл бұрын

Nice 👍

@vokuheila

Жыл бұрын

That's what he did in the video but you still have to do some work to produce all possible solutions. Just solving the quadratic is only a first step.

@SergioMiletto8

Жыл бұрын

Yeah i dont understand why everyone makes It likes its difficult but Is basic you get x=log base81 of 15(+-)2sqrt(129)

@italixgaming915

Жыл бұрын

@@vokuheila Once you have the equation t²-30.t+81=0 this is over. Looking at the coefficients, you know that the product of the solutions is 81 and that their sum is 30. So the two solutions are completely obvious: 27 and 3.

- لم افهم لغته ، لكني فهمت الحل جيدا ، فهذا معناه ان الرياضيات هي لغة الكون ، Thanks

In Russia we would solve it easier. Too much odd operations in my opinion (representation of 81 in the form of 3^4 at the first step, complicated solution of a quadratic equation (what was the purpose to factorize the equation after applying Vieta's theorem?), complicated finding of standard solutions for tabular sine values). But anyway I highly appreciate educational videos, as well as the efforts of the author to implement as much mathematical knowledge as possible in one video. Thank you 👍

@Vv3639ott

Жыл бұрын

How it's being solved in russia

@DashingData66666

Жыл бұрын

@@Vv3639ott 🤣

@Vv3639ott

Жыл бұрын

@@DashingData66666 kya hua😅. Socha kuchh naya sikhate honge vaha isliye

@user-ru9mo7ib2e

Жыл бұрын

А откуда этот преподаватель?

@user-oh5js9rl7l

Жыл бұрын

@@user-ru9mo7ib2e В описании канала написано, что из Танзании

This is probably the first Olmpiad Question I've thought, yeah I totally get that! The explanation is so clear and patient. Sometimes it feels like presenters want to show off how good they are. As a viewer, I genuinely felt you wanted me to understand. And it felt all the more genuine for the insufficiently large page conundrum!😂 Thank-you, 😊

AMAZING🌄

Two substitutions did the trick for me. First, let u = sin^2 x. A few steps later, let v = 81^u. Solve the resulting quadratic equation, then solve for v, and lastly for u. Find the values of x from there. It’s a little quicker.

Wonderful..... combining law of indices, trigonometry and exponential to solve mathematical problem

Very easy question.

todo muy lindo, pero te olvidaste de plantear para cuando u0 al usarlo como denominador, hay que plantearlo para operar y excliuir las soluciones

The best concepts applied in this question I am very excited

@learncommunolizer

Жыл бұрын

Thanks 🙏❤️

Consider the two expressions on the LHS: their sum is clearly 30 and their product is clearly 81. By Vieta’s formulae they are therefore the solutions of x²-30x+81=0, which are 27 and 3. Therefore 81^(sin^2x) is either 27 or 3 (since the equations are symmetric). Meaning sin^2x is either 3/4 or 1/4. Meaning sinx = ±π/3+2nπ or ±π/6+2nπ. Assuming a domain of 0=

@danielchmielewski2900

Жыл бұрын

How do you know all this shit 😅

@athiraa1718

Жыл бұрын

Yes u r right . But the guy in the video is simply complicating things

@otniel7370

Жыл бұрын

exactly

You can also cheack L. H. S =R.H.S by subtituting x=0, 30,45,60,90 (degrees) Then x=30, 60 (deg) It satisfies the solution

@DiHASTRO

Жыл бұрын

How to prove, that it's the full solution?

@tanish9682

Жыл бұрын

@@DiHASTRO it's and objective approach

@DiHASTRO

Жыл бұрын

@@tanish9682 if you just check exact values, it's not objective

@tanish9682

Жыл бұрын

@@DiHASTRO what I meant by that is. This is an objective approach because, in objective exams, you'll be given 4 options out of which one would be correct ( no doubt ). You just have you put the value of those 4 options in your question one by one and see in which option you get the left hand side of the equation equal to the right hand side of the equation. And whichever option equates your right hand side and left hand side is the right option.

@DiHASTRO

Жыл бұрын

@@tanish9682 now I got you. Really nice

I solved for one of the (many) solutions in my head and got x=60 degrees. Basically 81^cos2(x)=3 or 27 and all the solutions come from that.

تمرين جميل جيد.شرح جديد مرتب. شكرا جزيلا لكم والله يحفظكم ويحميكم ويرعاكم جميعا. تحياتنا لكم من غزة فلسطين.

@learncommunolizer

Жыл бұрын

Thanks and Welcome 🙏❤️🙏

Soal persamaan Trigonometri yang bagus ... Dengan menguasai Identitas Trigonometri, Persamaan Eksponen, dan Persamaan Kuadrat, maka akan didapatkan nilai cos x = ± ½ atau cos x = ± ½√3. Selanjutnya tinggal mencari nilai-nilai x yg memenuhi.

Wauuuuuu excelent resolution❤️👏🎯

@learncommunolizer

Жыл бұрын

Thank you!

4:41 NO need to separate -30u into -27 and -3...Just use Delta formula...Au²+Bu+C= 0 , where A=1, B=-30 and C=81... So Delta formula=> B² - 4AC = (-30)² - 4×1×81..=> 900 - 324 = 576... Therefore, 2 solutions : 1) (-B - ( square root of delta))/(2×A) (30 - ( square root of 576)) / ( 2×1) (30 - 24) / 2 6 /2 = 3 --- 2) (-B + ( square root of delta))/(2×A) (30 + ( square root of 576)) / ( 2×1) (30 + 24) / 2 54 /2 = 27 😊

@tikchbila_tiwliwla3869

Жыл бұрын

thats longer method and reqires a lot of calculations the P.S method is always easier if u spot it

Very good,,,, Nice

Excellent, sir

@learncommunolizer

Жыл бұрын

Many thanks

3^4(sinx)^2+ 3^4(cosx)^2 = 3^3 +3^1 First we will compare the exponents Sinx=±√3 /2 X=60° or 120° or 240° OR Sinx=±1/2 X=30° or 150° or 210°

@kumkum9073

Жыл бұрын

Well done👍

@abshirkilwe6707

Жыл бұрын

This correct and simple processes

@garethb1961

Жыл бұрын

Interesting. Correct answer, but I think it is incorrect! You have said that 3^a + 3^b = 3^c + 3^d implies a = c and b = d OR a = d and b = c. That is not true. Those solutions are indeed solutions, but are not unique. It only works in this instance because of the relationship between a and b.

@coolfreaks68

Жыл бұрын

Are you serious? 🤣

@thisumuthsa

7 ай бұрын

Can we put ± when we use radical sign

This is a very old AIEEE level problem. Also asked sometimes by NTA as well in jee mains in easy sets prolly.

@full-metal_zero0683

Жыл бұрын

Exactly!!! NO WAY this is an Olympiad level problem

@SushilKumar-gb4be

Жыл бұрын

if this is Olympiad level problem the I am Albert Newton

That is one beautiful equation

Never seen such precise explanations , you’ve gained a subscriber 👌

@learncommunolizer

Жыл бұрын

Thanks and welcome

@bubunsidhanta7882

Жыл бұрын

Bro atleast don't give so much gas to her

I have solved this question in class 10 final exams in 2011, boards exams were killer those days!! Indian things...

Nice solution, very useful.

@learncommunolizer

Жыл бұрын

Glad it was helpful!

Thanks for sharing

@learncommunolizer

Жыл бұрын

My pleasure

I like your detailed explanation of this solution👍🙂

@learncommunolizer

Жыл бұрын

Thanks and Welcome 🙏❤️🙏

VERY GOOD EXPIANAITION

During my schooling I didn't really like Maths. But now, I love learning maths to explore science & universe.

@RamanKumar-vz4fc

Жыл бұрын

Yes

The fact that I did this question just now while preparing for JEE exam and I had no freaking idea this was an Olympiad level question 👀

@SWExDeKu1454

Жыл бұрын

Why did u do this for jee? When do they ask these simple exponent questions? And btw, this question is nowhere close to a real Olympiad question, prolly a very low level Olympiad question

@GhoulZenoX

Жыл бұрын

@@SWExDeKu1454 while I do realise this ain't THE Olympiad question, but yeah this question is quite good when it comes to trigonometry equations, their general solution, identity, and basic maths all mix, bit confusing if u ask me but yeah it isn't even jee adv level prolly just mains

@bladman9700

Жыл бұрын

@@GhoulZenoX no it wasnt, in jee prep this comes under basic math and it is lecture example(I believe) , so seeing this that this is an olympiad question, and I didn't took me more than few minutes is quite suspicious. lol

@GhoulZenoX

Жыл бұрын

@@bladman9700 agreed this guys explained every small thing, otherwise it would've taken 2(average) mins only i guess

@dmwallacenz

Жыл бұрын

Obviously not an Olympiad level question. The title is a lie.

Great explanation sir ..... greetings from India ❤

@learncommunolizer

Жыл бұрын

Thanks and Welcome 🙏❤️🙏

Very good. Thanks 🙏🙏🙏🙏

@learncommunolizer

Жыл бұрын

Most welcome Thank you too!

I really liked this problem. I taught trig for quite a while and I would have taken quite a bit of time to get this. I definitely wouldn't have solved it on the fly in class.

Wow fantastic❤

@learncommunolizer

6 ай бұрын

Thank you very much!! 🤗

Very nice 🎉

@learncommunolizer

7 ай бұрын

Thank you very much!!

Hi. What if you just consider using, e.g., pi/3 + k*pi instead of pi/3 + 2*k*pi, 'cause it will lead you to positive and negative values as well, therefore, it would take only half of the equations for x. Also, the second one would be 2pi/3 + pi*k, leading to positive values (second quadrant) and negative values (fourth quadrant).

@craigoloo857

Жыл бұрын

Using k*pi is wrong as that will lead you to negative sin values which are not correct for the first solution of +(√3) /2 I mean in terms of the values of x that apply, you're correct, but remember we're trying to show solutions to specific terms, and in this case are terms that bring positive √3/2 and the terms that bring negative √3/2. These are essentially 2 different equatiins thus require 2 different sets of answers i.e a set that only solves for positive values and a different set that solves for negative values

@rickdesper

Жыл бұрын

​@@craigoloo857 Both sin x and cos x are squared in the original equation. It doesn't matter if sin x < 0 or cos x < 0.

@MsGinko

Жыл бұрын

@@craigoloo857 k*pi would give rise to 4 solution forms, whereas k*2*pi are 8 solution forms. Both are equivalent. k*pi solution forms comes from solving the identity sin^2(x) = (1-cos(2x))/2

I love such a tricky question

Very nice video Learncommunolizer!

@learncommunolizer

Жыл бұрын

Thank you! Cheers!

hellow from janan . This is the first watching! Your commentary is so polite!

Very detailed explanation ☺️📌

@learncommunolizer

Жыл бұрын

Thanks a lot 😊

Very nice bro

@learncommunolizer

Жыл бұрын

Very nice

Consider using logarithmic laws: ln(81^sin^2x + 81^cos^2x) = ln30 into sincos^2xln(81) = ln(30) sin^2(1-sin^2x) = ln30 rearrange and solve using quartic formula and find answers within domain

@Emellstornn

Жыл бұрын

Хоть кто-то вспомнил про логарифм.

short cut notice 30=27+3=3³+3=3^(4ss)+ 3^4cc guess 4ss=3 , 4cc=1 adding confirms c and s are cos and sine of the same angle but can be interchanges d so c=1/2 s=sqrt(3)/2 arccos 1/2 =60⁰ arcsin 1/2 =30⁰ which are two alternative values for x but also negatives also because of the squares and circularity. so in the end x=45n±15 n/=0

Nice job. Impressive.

@learncommunolizer

Жыл бұрын

Thank you! Cheers!

Jee mains ka question

Good

Thanks, verry good

It's a beautiful conclusion.

@learncommunolizer

Жыл бұрын

Thanks and Welcome 🙏❤️🙏

thank you sir...

Quite basic and quite easy. Remember solving such problems in under 5 mins in junior college

nice explanaton

@learncommunolizer

Жыл бұрын

Thanks and welcome

Amazing regards from India

Thank you for the video.

@learncommunolizer

Жыл бұрын

You're welcome

I love and hate how I can understand each step on their own but I could never have solved the entire equation by myself.

@pentagon-math

Жыл бұрын

youtube.com/@pentagon-math

Loving this guy

@learncommunolizer

Жыл бұрын

Thanks ❤️🙏

この人の英語は聴きとることが易しいので助かります

Good explanation. This kind of equations where it is used. Could you give some applications.

Nice trick

@learncommunolizer

Жыл бұрын

Thanks and Welcome 🙏❤️🙏

Congratulations!

Nice. . ❤️❤️❤️

@learncommunolizer

Жыл бұрын

Thank you! Cheers!🙏❤️🙏

Very good

@learncommunolizer

Жыл бұрын

Thanks! 👍

Perfect detailed explaination for the learners. But I'd like to point out some errors when you list out all the x values. For Sinx=+√3 /2, x should be π/3+2πk and 4π/3+2πk (not 2π/3+2πk ); for Sinx=-√3 /2, x should be 2π/3+2πk and 5π/3+2πk (not 4π/3+2πk ). For Sinx=1/2, x should be π/6+2πk and 7π/6+2πk (not 5π/6+2πk ). For Sinx=-1/2, x should be 5π/6+2πk and 11π/6+2πk (not 7π/6+2πk ).

Good trigonometric equation! Thank you!

@learncommunolizer

Жыл бұрын

You are welcome!

Great video, now I want to know how to solve the one who setted the question?😇

Watching as nostalgic Remembering beginning of mechanical engineering graduation 👏🏽👏🏽👏🏽🇧🇷🇧🇷🇧🇷

Good job 👍 I liked the video, good for newcomers to trigonometry. It doesn't use too much higher concepts which is nice. (Although I prefer more complex concepts for the same question) Although this proof was really nice and I like the format in which you write, I'd still say it's too slow of a method for olympiads, 16 minutes per question for an olympiad is really bad, even if it's 3 hours long. The proof is long too, entertaining to see but too much to write. I suggest using other trigonometric properties like cos²(x) - sin²(x) = cos(2x), which you can use by taking out sin²x from both of our terms with exponents. It would have made it slightly faster. A few comments also suggest other methods which are nice too, that can be applied too to make proving solving. But overall a nice explanation and nice video for someone with just basic information.

@AttachmentStudios

Жыл бұрын

In case you are using the cos(2x) method I suggested you can later also use log and its properties to calculate 2x really fast and half it to get x.

@yvesdaoust9554

Жыл бұрын

u+81/u=30 is nearly immediate and the solutions 3 and 27 found by inspection.

@kfibcudwiefjw7428

Жыл бұрын

Yeah this guy took three lines to explain the product-sum method lmao😂

Mentally I have got that sin^2 x is either 1/4 or 3/4. That is x would be 30°, 60° each of them added to plus or minus a multiple of 180°. Thank you very much!

@rickdesper

Жыл бұрын

That only gets half the solutions. You also have solutions in the 2nd and 4th quadrants. You need to say "multiple of 90 degrees."

a=sin^2(x) 1-a=cos^2(x) 81^a + 81^1-a=30 we can write 30=27+3 and we can give 27 or 3 to 81^a or 81^1-a when we do this 81^3/4 = 27 and 81^1/4=3 sin^2(x) can be 1/4 and 3/4 sinx can be +-1/2 and +- sqrroot3 / 2 from these roots x can be 30+360k,60+360k,30+180n and 60+180n but n is form of 2s+1

@chanboiiii

Жыл бұрын

* +- √3/2

@bbt584

Жыл бұрын

@@chanboiiii thanks

Ooh… I remember learning this one in high school That u is so nostalgic…

This is interesting! Especially, 4:54 when you use factorization in quadratic equation for 'u', it is similar with my country's factorization which is learned in 9th grade. I think Math is same wherever.

@uwuuwuwuwuwuwuwuwuuwuuwu

Жыл бұрын

폭립 맛있어요

5:08 ahhh viet's formulas, you are a man of culture as well

@macieklis7512

Жыл бұрын

And i think u forget to put u>0 when u introduced this variable

I got the same answers. There is another way. Just a bit simpler Multiply both sides of the equation by either 81expcosinesquaredx or 81expsinesquaredx. Just remember that cosinesquaredx + sinesquaredx = 1. You'll arrive at the same answer.

Nice job!

@learncommunolizer

Жыл бұрын

Thank you! Cheers!

Very good...but the hard way

Standard engineering entrance exam problem [complexity level :- low ]. Got some basic concepts revised , Thanks for it.

I am in class 10 and easily solved this problem proudly from india

4:00 don't forget to say that you can multiply the both sides by u because u is never 0 (u=3^{4sin^2 x} which is never 0). Because if you multiply both sides by 0, you don't resolve the same equation (if your equation is 2u=1, then you multiply both side by u, you obtain 2u^2=u, then u(2u-1)=0, which has two solutions : u=0 and u=1/2, but u=0 is not a solution for the first equation 2u=1).

Idk which is more mysterious, how you solved the problem (Only took Algebra 1 and Geometry in high school and Quantitative Analysis in college), or why the algo thought this would be a good video to recommend.

THANKS PROFESOR !!!!, VERY INTERESTING !!!!

@ahmadmatter5612

Жыл бұрын

Basic mathematics nothing un usual

@user-tb8lg5jo1u

Жыл бұрын

@@ahmadmatter5612 ok, and?

I am from India. Nice tutorial 👌👌😊

@learncommunolizer

Жыл бұрын

Awesome! Thank you so much 😀 and welcome 👍👍

May I ask you what's the name of the pen you used?

For indians who are preparing for IIT JEE exam these questions are like confidence booster

@prathameshbhagat7797

Жыл бұрын

Very true

thaks

Hello, I love your channel. I love Mathematics 💘. From 🇮🇳

@learncommunolizer

Жыл бұрын

Awesome! Thank you!

Easy Problem I am preparing for jee and just with my class 10 knowledge i solved it.

Seeing the equation (but not watching the video), I wondered what's so trigonometric about this quadratic equation. With cos^2(x) = 1 - sin^2(x) and u = 81^(sin^2(x)), we get: u + 81/u = 30 or u^2 - 30u + 81 = 0, which gives u = 15 +- squrt(15^2 - 81) = 15+-12 u = 3 or u = 27 From u = 81^(sin^2(x)), we get ln(u) = sin^2(x) * ln(81) and thereby sin^2(x) = ln(3)/ln(81) or sin^2(x) = ln(27)/ln(81) For x, we get x = +- arcsin(squrt(ln(u)/ln(81))) with u either 3 or 27, and the solutions those x that fulfill the original equation after checking. Let's watch the video, if I got it right.

Very nice👍 I want to prepare my daughter for it.

@learncommunolizer

Жыл бұрын

Great 👍 All the best

Good job

@learncommunolizer

Жыл бұрын

Thanks

Dg cos^2x=1-sin^2x menjadi pers kuadrat...dst

sinx^2+cosx^2=1 then given equation is 81^t + 81^(1-t)=30, left 81 = 3^4 then 3^(4 * t) + 3^(4*(1-t))=30 if t=1/4 left = 3^1 + 3^3 = 30. fin

Another method of doing this is if you convert everything to have a base of 3 then equate the power, the 30 becomes 3^3 + 3^1

ThanQ sir.I like Algeobra.

Güzel çözüm yaptin

I have been enlightened.

@learncommunolizer

Жыл бұрын

Great! Thanks 🙏❤️

I was good at math in high school, but that was a long time ago. What does sin²x mean? The sine of x, then squared? As opposed to the sine of x²? But wouldn't that just be (sin x)²?

Nice problem!

@learncommunolizer

Жыл бұрын

Thanks!

Obrigado! Thank you!

@learncommunolizer

Жыл бұрын

Thanks 🙏👍