Prove that 🔥 cos (x + y) = cosx cosy - sinx siny 🔥 Full derivation by
ฝัง
- เผยแพร่เมื่อ 15 ก.ค. 2024
- Hey students!!! 🧑🎓 🥳 🤠 👏 👩🎓
You will learn the derivation of a very important trigonometry formula (identity)
cos(x + y) = cosx cosy - sinx siny
in a very easy and simple way with the help of simple animations and colorful explanation. The formula is one of the basic formulas that is used to derive many more trigonometric formulas. So it becomes extremely important for students to understand the underlying concepts as well.
This derivation of this formulas includes 3 important parts (steps):
Finding coordinates of 3 points on Unit Circle making angles x, x+y, -y on the centre of the circle
Identifying 2 congruent triangles using these points
Using distance formula to eventually derive the formula.
I hope you will find this video really helpful. Let me know your thoughts on this video tutorial in comment section.
00:00 About the derivation of the formula
01:14 Quick tip
01:50 Finding coordinates using Unit Circle
05:49 Prove triangles are congruent
09:24 Applying Distance Formula
#trigonometry #class11maths #class11mathsolution #trigonometricfunctions #trigonometricformula #cosformula #mathsbysunilsir #mathsbysunilsyal #mathemafia #trigonometricidentities
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thank you so much sir✨ you helped me to get 6 marks without any doubt thanks a lot sir 🙏✨❤️🥺
My pleasure 👍 please share it 🙏
All the best for your tomorrow's exam 😂😂😂😂
😅
Nahi Bhai ajj hain
Watch complete chapter 3 (Trigonometric Functions): th-cam.com/play/PLHipvIKLGDdcH1Nb_4Fr78gwG8rr9v1qM.html
Barabar ❌ Brabar ✅
Apart, Nice Teaching I Understood 👍🏻
Punjabi hoon na ... Is liye naturally aise bolta hoon .. barabar 😎
Supper teaching sir
thanks , very useful programme
Thanks for this wonderful explanation sir ❤. In my book its not explained this easy.
Thanks 😊
Very simple and excellent explanation.
Many Thanks sir.
Thank you sir the only video where we get to understand clearly why cosx and sinx as co-ordinates
I know this is always hard for students to understand. That's why I generally explain this in every relevant tutorial. Glad this tutorial is helpful. Pls share if you don't mind. 🙏
Tq sir very intresting and esy method teach you sir and we all request sir more videos you send sir
Thankyou sir
Thank you so much sir for clear explanation.. ur teaching is very understandable.. helped me alot.
I am glad it helped. If you don't mind, pls share it with your classmates. I will really appreciate it. 👍
Suberb and concise explaination. Thank you so much sir ❤
Sir please make video for other chapters and for class 12 math🙏
Aap bahut achchhe se samajha diye hai. Thank you
Glad you liked it. It took me a lot of time to create this video. It would be great if you share it with your friends. 👍
Thank you sir,u made it complex to simple
My pleasure dear. Please share if you don't mind 👍
Thank youu sirr i came just 1 day before my exam and u just clear my douts so easily hats off to you sirr
My pleasure. Best of luck for your exam. 👍
Thank you sirr..
Same here
Very satisfied by your teaching sir i hope you deserves more subscribers
Thanks for your good wishes. I have spent almost a week to think and prepare to explain this derivation. The derivation given in the book or on internet is quite complex and I did not like that. So I thought of explaining this concept in the simplest possible way. I hope more students would feel it helpful. Cheers!!!
nicely explained video!
Pls share it 🙂
Thank's sir
Pls share it.
Thankyou sir ❤
You are most welcome. I feel that I have put a lot of efforts in this tutorial. It will be really great if I share this video with your friends. Cheers!!!
Tq ssooooooo much
Most welcome. Please share it 🙃
Hello sir how are you doing
Sir if you remember me i have seen your videos from starting of the channel
Glad to see your channel growing sir
I just wanna give you an advice sir that you can start class 11,12th applied math classes and this can help you a lot in growing
I do remember you Hardik :) Thanks for supporting me for so long. I really appreciate it. Also, I feel really happy that you have shown concerns about my channel and want it to grow more and to really great heights. I have started focusing on class 11 as of now and would like to stay focused on it for a while. I may create different videos in between but primarily class 11 be the focus. Anyway, what about you? What are you doing now? What subjects are you studying?
8:10 Sir, sign se fark nhi padega kya? Magnitude/Quantity same hai sign(direction) alag hai... So x+(-y)?
I hope you are asking about the congruence. If so, we only take the measure of the sides and angles and not the signs for congruency. Imagine 2 different sticks, each of length 3 meters, lying on a plane. We can pick any of these two and place it over the other stick completely overlapping it. Hope it's clear now.
Hoping sir next time you had 1mil subscribe
Thank you sir for helping me in 10th class
Thank you and welcome. :)
A point ke coordinates to barabar samajh aa gye ... Pr , B ke kaise aaye.... x+y>90° hoga to vo to right triangle bnega hi nhi to usme trigo lgegi hi ni to B point ke coordinates {cos(x+y),sin(x+y)} kaise aaega
Watch this part. You will get it.
th-cam.com/video/MhOqR2l5h6w/w-d-xo.htmlsi=E2nmTM9RD3GVRDli&t=233
Sir is the distance formula correct ?
what is your doubt?
But sir the distance formula is √(x2-x1)²+(y2-y1)²
Is there any issue in the video?
Sir distance formula toh (x2-x1)²+ (y2-y1)² hota hai aapne (x1-x2)²+(y1-y2)² karwaya hai
(2-5)² aur (5-2)² kitna hota hai ... 🙂
I have a dout
How -cos(-y) becomes -cosy, it should be +cos y ?????
Watch this video: th-cam.com/video/Xkyvz4knDew/w-d-xo.html
You will get it.
cos(-y) = cos y (it is given in NCERT)
then multiply both sides by -1
We've -cos(-y) = -cosy
Cosx+y and sinx+y coordinate kis logic se bana
Can you explain your query? Also mention the time as well?
@@Mathemafia4:11 me coordinates cos(x+y),sin(x+y) kaise hua kyuki waha par koi right angle nhi ban Raha hai
Aap kiska ka reference leke coordinates nhi bata skte hai
Watch this tutorial from 3 : 30 onwards. You will get the answer you are looking for.
th-cam.com/video/MhOqR2l5h6w/w-d-xo.html
@@Mrdoubt-xu1ee If you still have any doubt, let me know. I will try to explain.
Distance formula is wrong
Kaise?
Yes distance formula=√(x2-x1)2+(y2-y1)2
(x2-x1)² is same thing as (x1-x2)² as (x2-x1)² = (-1(-x2+x1))²
Exponent law (ab)^m=a^m × b^m
= (-1)²(x1-x2)²
= (1)(x1-x2)²
= (x1-x2)²
Similarly for y
Thank u sir
My pleasure. Pls share with your friends if you don't mind. :)