97% Students Answer This Trigonometry Question Wrongly !
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- Опубліковано 9 жов 2023
- This simple trigonometry question is mostly answered wrong by students, Let's learn why?
Let's check out the complete solution.
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This question deserves to be the most hated problem of trigonometry
Phir sir ne kya bola wahi to bola hai 🙄
4 step mein hogaya 😂
Naa!!
@@shoyo_Ishida solution chaiye
@@aakritkatyal9135 noop!!
Sir, i saw your video on the same problem and the next morning when i was searching for the video, i didn't find it anywhere, not even in my history, but then i thought that you might have deleted the video. Thanks for re uploading the problem.
Same with me😅
very well explained and nice approach. thank you!
Long but predictable method: sin (kpi/m), k=1..n are roots of equation sin(mx) = 0. So we expand sin(mx) in powers of sin(x) to get a polynomial equation in sin(x) of degree m. For m = 7 we get:
sin(7x) = -64sin^7(x) +112 sin^4(x) -56 sin^2(x) + 7sin(x) =0. We can eliminate sin(x)=0 as solution, so the products of the remaining 6 roots is 7/64. This product is square of the required quantity.
Did you "predict" the method prior to looking at the solution?
Yeah bro same 😂 I once was curious and derived sin5x , 7x 9x 11x and those r some neet results if u want an interesting question check this .. what is the coefficient of last 3rd term of sin101x given that it's expansion is organised on the basis of descending order of powers of sinx ... Sayd question smjh me aagya hoga kya bol rha ....
Actually mein general term ka coefficient khoj rha tha nahi mila but kuchh terms me pattern mila
Hey please tell which theorem or Formula you have used, please tell the name 😢
We can use complex numbers where w = cos(2pi/n) where w is nth root of unity
As a matter of fact sir , I have solved this problem during my JEE days and have come to IIT BHU after qualifying JEE23 . Thank you sir for bringing out such problems
Hey did you solve this by this method only ?
Sale flex maar. Rha h tu
@@itsshubh3430 If he really did this tough problem all on his own he can flex and deserves the honour,kudos to the guy👏👏
Congrats bro❤
Q@@😊@😊
Maza aa gaya sir,
Definitely looking up for more such videos❤
"BHANNAAAAT IS A ICONIC WORD"
LOVE YOU SIR❤❤❤
Complex numbers se kijiye alag swaad aayega. (use 7th root of unity)
In general , it can be proved using complex numbers that: multiplication of 'N' terms of sines where each acute angle is in A.P. such that the first term is equal to common difference and last term is just less than π , is equal to (N+1))/2^(N).
In the question in this video , let the value to be determined be X . Then , X²= sin(π/7)sin(π/7)sin(2π/7)sin(2π/7)sin(3π/7)sin(3π/7)
Now using sin(x) = sin(π-x) , we have ,
X^2 = sin(π/7)sin(2π/7)sin(3π/7)sin(4π/7)sin(5π/7)sin(6π/7)
The last equation follows the formula above , hence , X^2 = 7/2^6 = 7/64 . Take square root and you get your answer.
What should I put in the value of N
@@Raj_Sharma_007 As written above , N is the number of terms.
Acha , thik h
Hello :)
I wanted to know how you came to know about this identity, because I am halfway through my 11th std., starting the chapter 'Circles' tomorrow, and I never came across such an identity while studying the two trigonometry chapters in the past. Thanks.
Thank you for this trick
Good evening sir.Sir pyq solving videos please
Req to you sir..pls start PYQ solving of last 3-4 years Maths
why video was deleted and reuploaded sir?
As a student of 10th class, I think trigonometry is used more in making questions harder , instead of finding length of a building.😂😂😂
Edit:Oh my god mai toh famous ho gya.
Yes you thinks😂 correct
Bilkul shi pakdo ho munna
😂😂😂😂😂
it will make your analytical and critical thinking stronger... which are basics of logic development
No, we use trigonometry in physics at an advanced level, therefore these difficult problems help us in that way.
Well explained sir!! I appreciate your effort 😊👍 But sir ,,i have an another excellent approach,,which is luckily a brilliant and time saver approach for this particular question!!
We have a formula ,,,sinπ/n .sin 2π/n .sin3π/n ...
.sin (n-1)π/n = n/{2^(n-1)}.
In this particular problem we have value for sinπ/7 sin2 π/7
...sin6π/7 = 7/(2^6)..
Now we let us assume sin π/7...sin3π/7 =X .then the next three terms can be transformed in terms of Series of X.as eg:-sin4π/7 =sin 3π/7..now the series become X^2 in LHS...now apply root both side .we get value as √7/8..
Its so simple,,can be done within 4-5 lines😊😎🔥🤘 Lets have a look to my approach! Hope u like it !!.
Thankyou!
Radhe radhe🙏
Could you pls share with me a link for the proof of this formula, or just hint me the approach to prove it? Thanks
@@shauryagupta3644i appreciate your curiosity 😊!! And thankyou for read my approach 😊 .
To be honest ,,this formula is not related to intermediate level directly!! And the proof is so lengthy ,you have to use eulers identity ,concept of limit ,and little bit use of complex no. Yeah iam also an iit jee aspirant right now😊 so ,no doubt you can understand the whole proof almost ! But this will worthless for u right now !! The result is important ,,so plz try to keep that result in mind ! Remember,,you cant use this formula in every situation,,the major condition is the coefficient of π in last term is 1 less than the denominator !!and the product should be continuous!! Further modification in this formula led to the result of "Riemann integral ". But still you want to know the proof ,,i have done an effort in searching the video you need to get the proof . Iam providing you link ,,you can chek it out!😊👇
ua-cam.com/video/hQ532SjbxNo/v-deo.htmlsi=auUbzdDu8AipVGw_
This contain the proof u want,,and given by any university professor !!👍.
Once again ,i say ,,result is important!! Thankyou to love my approach!!😊👍
Radhe radhe 🙏
@@shyamaldevdarshan thanks I applied without knowing proof definately gonna learn proof after my complex number course.
@@timewalkwalker welcome! Yeah sure! You can learn😊👍
Radhe radhe🙏
Yes
Nice Explanation Sir.
but I have another approach for this question
as we know that CONTINUED PRODUCT(k=1 to n-1) sin(kpi/n)=n/(2^(n-1)
HERE S= sin(pi/7) x sin(2pi/7)x sin(3pi/7)
S=sin(6pi/7)sin(5pi/7)sin(4pi/7)
=>S^2 =CONTINUED PRODUCT(k=1 to 6) sin(kpi/7)=7/2^6
=>S= sqrt(7)/8
HOPE U LIKE IT!!
THANK YOU
Yes. It's a general formula which can be easily proved using complex numbers and a little bit algebraic manipulations.
This is exactly what i thought when I saw this.
Can we get in touch please I think u can help me in mathematics.
Your solution seems to be based on an interesting topic can you tell me more about that and for me there are some things that are unclear in your solution like how is s is equals to 2 products which are different I mean can you elaborate your solution
@@Player_is_I First, it's S^2 . Note that after squaring, each terms on RHS appear twice so that now we have a pair of each term which was present in S. Now , take exactly one term of each pair and use the identity sin(x) = sin(π-x) to get the desired product.
You are the best guruji, thanks for the question practices ❤❤
When we got 8xy=x, why can't we do this to find x 👇
8xy-x=0
x(8y-1)=0
x=0, y=1/8
It would've been much faster
wrong if y=1/8 x can be any value
@@adarshsubramanian9560 bro xy = x/8 wat are you talking about
@@yxsh5033 For example if y=1/8 then if u take x value as 1 then also equation is satisfied
because x is not equal to zero
Very nice sir. Quite inspirational solution
Super explanation sir 👍🏻👍🏻👍🏻👍🏻👍🏻👍🏻👍🏻👍🏻🥳🥳🥳🥳
Sin m^n=? ( No expansion, should be FINITE SERIES.)
Can also be done by complex no
I have created formula see here for n=7 x=√7/8=} x^2 = 7/(8^2)
And for n x^2=n/(2^[n-1]) ...😊
Yeah easiest method
Sahi bola sir, formula hai sara yaad pr question nhi bn pata mere yaar
Appriciate for those student who solved. This question 😮
Bruh it's a basic question 🤖
@@MehtabHussain-vh3bljee also ask basic question
sir have very fast solution for this with complex no there is a trig identity of sin(pi/n) *sin(2pi/n) .... *sin((n-1)pi/n) = n/2^n-1
now keep n = 7 and now sin 4pi/7 is same as 3pi/7 and so on therefore
ans = sqroot(n/2^n-1)
The basic orthogonalality of sine waves is demonstrated here.
Kya sir ne yeh video doobara post kra hai isse pehle yeh video sir ne kya post Kiya tha jo delete kr diya tha koi batao
Sir apse defense ka preparation krna hai kaise kre ❤
Reupload?
Different approach - for series that is in product and is in form of sin theta we can use √2n+1/ 2^n . N - no of terms
Use of complex no
Abe chup gawar
Wow!
nobody will mind even if you also declare it as the most hated question in JEE level.
We love you sir❤
power of aman sir- only 525 views and 106 likes❤🔥❤🔥❤🔥❤🔥🔥🔥🔥l
ध्यान से देखो😂
My whole high school life ended learning this sin-π cos-π but still i dont know where to use this math formulas in my daily life.
There's one more method
∏^n−1k=1sin(kπ/n)=n/[2^(n−1)]
we need to find sinpi/7.sin2pi/7.sin3pi/7
but to use the formula Given above we need to have 6 terms as k goes from 1 to 6
we also know that sin(pi-pi/7)=sin(6pi/7), sin(pi-2pi/7)=sin(5pi/7), sin(pi-3pi/7)=4pi/7 so
we can say that [sin(pi/7).sin(2pi/7).sin(3pi/7)]^2 = ∏^6 k=1sin(kπ/7)=7/[2^(6)]
so now we can take root on both the sides and get our answer as root 7/ 8
Awesome ❤
Ans the proof of that formulae comes from complex numbers
Can you please explain that to me 😅
@@slimshadyff7848 explain what? We only need to use the formula for this method, but the problem is most of us aren't aware of this formula. To calculate answer using the formula we need to make sure that we've 6 terms as the formula requires us to use from k=1 to k=(n-1) here n is 7 so k will be 6. Rest is basic, sin(pi-x) = sin x as second quadrant sinx is positive
@@hretzbro pls can you give name of the formula so that i can learn it .
Sir please derive formula . I always mug up and can't understand relationship between the formula . √( s . S- a . S- b. S- c)
Just search for derivation of Heron’s formula
It's easy you can find so many videos on it in English and may be in Hindi too
Can u please solve this question using quadratic equations/polynomials?
Good qustion sir jeee namste🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
U teach so well that MATHEMATICIANS will try to learn from uuu❤❤❤...
Sir wat is math?
Sir kya ye question class 10 ke liye bhi hai
Sir please solve jee main 2023 1st feb shift 2 sequence and series question 🥺🥺🥺
You should also prove why you took the positive part
Sir ne bhot bade tarike se karvaya hai
Sir iat exam ke upper video bannaie
😅
5:20 x zero nahi ho sakhta aapne kaise judge kiya sir? Plz batadijiye.
Kyunki sin. 0 180 360 me hi zero hota hai baki jagah nahi
@@neerajprajapati3852 bhai lekin x toh multiplication of sin fn hai toh vo zero bhi ho sakhte hai.
@@wipergaming1448 dekho anuj yahan sin p/7 sin2p/7 sin3p/7 ki bat hai aur ye teeno non zero hain aur teen non zero quantity ka product bhi non zero hi hoga
Bekar
Sin ko cos me covert karo aur
CosA cos2A cos4A....= sin2n/2nsina
For such ques....Complex no. God
2 ko 4 time multiply karne se 8 kaise hoga sir.
Can also be done by complex no.
Very easy question of complex no.
5[1.96-sin^2{(cos^-1 (0.02)}° ] find the value of it . Challenge to you sir 😊😊😊.
I am read in class 9
As this is a IMO problem.............So This should be one of the hardest problem....
Sir wbjee k liye kuch class hota to acha hota
Excellent sir
Thanks
Maza aagaya sir but itna time kidhar hai solve karne ke liye ek question ko
Actually, this question is from a book named A das gupta
Re-upload 😊
Toh last time the answer was wrong as he forgot to multiply by 8
If I get this question, thsn I will focus on other problems than this one. IIT JEE failed person (rank 2k in 2004) this side..lol
Probably justifies why I didn't qualify for IIT but doing better than 50% IITians by knowing how the world money flows.
So how exactly does money flow
Assumption ka game hai...
Legends ->> repload
Solved it...!... Loved the problem... I tried straight for two days for it 😂
अतिसुंदर❤
Sir isko complex no se kiya Jaye to 2 min me ho gayegaa
Sir apke questions ❤❤❤❤
"Maths approach ka game hai " 🔥🔥
भाई मुझे तो पता ही नहीं था l
Thanks for telling .
sir 3 step ma aap ye jo tod te ho ye samaj ma nahe aata ha jesa ke aao ne 4π/7 ko 3π/7 likh diya 😢
Mast aproch ha
Mere se same question par cos wala ho gaya tha
Put value of sin 180
Mast hai sir
Inelegent Solution
Sir please NDA ka batch start kr do yt pe please sir😢😢😢😢🙏🏼🙏🏼🙏🏼🙏🏼🙏🏼🙏🏼
❤❤❤❤
Kya sir apply formula of trigonmetric series😮
Bro there is only formula for continued product of cosine series and not of Sine series
❤
π\7 ka square kyo nahi kiya
legendary, 2 saal purana doubt solve hogaya
अब और maths पढने का मन नहीं कर रहा हैं sir,, 😴felling tired...
❤❤❤
Thank you sir
Biggest question is that is trigonometry useful? Mostly no.
Solved using complex numbers
Sir sin(2pie/7)=sin(5pie/7)
As we take 7@=(2n-1)pie
We can make sin4@=sin3@
Expanded to
°4cos@(1-2sin²@)=3-4sin²@(because sin@=0 is rejected)
°then squaring both sides
16(1-sin²@)(1-2sin²@)²=(3-4sin²@)²
°-64sin⁶@+128sin⁴@-80sin²@=9+16sin⁴@-24sin²@
°64sin⁶@-112sin⁴@+56sin²@-7=0 (is the equation in which if we take roots in form of sin²@, roots are sin²(pie/7),sin²(3pie/7) and sin²(5pie/7))
Lets comment on the values for all three angle sin give positive value )
From equation produts of roots in form of sin²@:
sin²(pie/7)sin²(3pie/7)sin²(5pie/7)=7/64
Then
sin(pie/7)sin(3pie/7)sin(5pie/7)=square root (7) /8
Sir I did this please see this one time sir .
Sir ... is it the only solution for this question..... if any solution is there please tell
Apply direct formula for product series
Check my comment 😊👍
@@shaatirop8901WHAT??WHICH FORMULA
Approach + formulae
I learnt trigonometry in the early 70s.Now a retired banker.
You said that the problem is with the approach, and not with formulae. Right?
My question is why does my approach gets to be wrong.
It was incorrect 50 years back and is incorrect even now.
I don't think it was too hard because your have think approach of this question by basic mind.
Haan me yahi video dekhna chahata tha
Re-upload
"X ki tasal" was epic😂😂
This question is given in amit m Agarwal trigonometry
As a 12th class student i can guarantee guys this is nothing . If u are an engineering student u have to been through a lot .
I can guarantee you could not have solved this problem had you not seen the solution in advance.
So this problem is SOMETHING.
Sir you can solve using π/7 property 4π/7=π -3π/7
It will give ans in 2 steps
Sinπ/7 sin2π/7 sin4π/7 multiply divide by 2cosπ/7 and it will give ans 1/8
Abe simple Sai question cengage se dal diya formula based question tha yarr dead easy
11th me 22.5° ka value batane ngi sikhaya gya ,, so difficult to lagega hi😣😣
Sir ek hi video do bara
Arjuna 1.0 adv lecture tarun sir ne iske 3 methods bataye the 7 months pehle 😂
Pr sir na ak method se solve krdiya it's talent😂
is porey question mein y ka trick hein
Use complex number