Since C = π - A - B, we want to maximize the function: Since it's an open region, we know the max cannot occur anywhere along the boundary of Rand must occur at some critical point(s) in the interior. Answer by stanbon(75887) (Show Source): I was looking at this question which asks for the minimum value of $\cos A + \cos B + \cos C =\alpha$ and the answers there state that the minimum value is $1$. are solved by group of students and teacher of JEE, which is also the largest student community of JEE. In triangle ABC, find the maximum values of cosA*cosB*cosc? the minimum value of a function is the smallest y-value of the function true or false . Proof? So, the maximum is when sin(x) = sin(a-x), therefore x = a - x and x = a/2. soon. cos 12° cos 18° − sin 12° sin 18° And Find its exact value. The value of cosA + cosB + cosC in a triangle is less than 3/2 . KevinM. Trigonometry Formulas Table and List . 2 c. 0 d. 8 Q.5 The least value of cos2 -6sin .cos +3sin2 +2 is a. Proof? If sinA + sinB = a and cosA + cosB = b, find the value of tanA-B/2 . Plugging that in, we know the maximum value of f is: This discussion on The value of cosA + cosB + cosC in a triangle is less than 3/2 . Proof? 4 10 b. Math. are solved by group of students and teacher of JEE, which is also the largest student community of JEE. community of JEE. if cos(B-C)+cos(C-A)+cos(A-B)=-3/2 then prove that cosA+cosB+cosC=O and sinA+sinB+sinC=O after that prove that cos(B-C)=cos(C-A)=cos(A-B)=-1/2 . 8 9 b. Is translation of position vectors allowed. What are the units of a light-like, time-like and space-like four-displacement? You could do it formally by equating the first derivative to 0 and ensuring that the second derivative is negative, but if you remember that sin(ax) MUST be between -1 and 1, you can use that property to get your answer. Hii Piyush Look in case of triangle... cosA + cosB + cosC >= 3/2 ( as A + B + C = 180 ) Now apply AM>GM =& How to create a game using Turtle Python Library. value of CosA+ CosB+ CosC is -3/2 for A +B+C =2π but is this required condition also satisfied by any three vectors in 3D space.? asked May 2, 2019 in Mathematics by Niharika (75.6k points) Question 768377: (1+cosA)(1+cosB)(1+ cosC) = (1-cosA)(1-cosB)(1-cosC) Show that one of the values of each member of this equality is sin A sinB sinC. (we can prove it easily) P: the absolute value of the largest of the differences between one of the first 10 rates and the average daily rate of the tests. Active today. Learn in our Free Webinar. If A+B=C, Prove that cos^2A+cos^2B+cos^2C=1+2cosA.cosB.cosC? 5 - 4sin(3x) will have a maximum value of 5- (-4) = 9. over here on EduRev! prove that sinA/(1+cosA) + (1+cosA)/(sinA) = 2cosecA = -1 - 2 cosa cosb cosc + 2cos^2(a) cos^2(b) - 2sina sinb cosa cosb = -1 - 2 cosa cosb cosc + 2cosa cosb (cosa cosb - sina sinb) = -1 - 2 cosa cosb cosc + 2cosa cosb cos(a + b) Cool problem. I know, min. Lv 7. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … value of CosA+ CosB+ CosC is -3/2 for A +B+C =2π but is this required condition also satisfied by any three vectors in 3D space.? Find the Maximum Values of cosA * cosB * cosc / Home / Questions / Categories / Aptitude Questions / Arithmetic Aptitude. Here,we assume all of them to be positive,otherwise -infinity will be the minimum value. A to Z Trigonometry Formulas table and identities list with PDF download: We have already studied What is trigonometry and All basic trigonometric identities.Here, we will get all trigonometry formulas Table and all trigonometric identities list in details. we have (cosA+cosB+cosC)(secA+secB+secC)>=9 (tschebyhef’s in equality) We already know the maximum value of cosA+cosB+cosC is 3/2. Proof? By continuing, I agree that I am at least 13 years old and have read and Pre-Calc. Asked … The Questions and This also excludes A=0 as a solution, since A=0 is in the boundary of R, which is not a part of our valid region. Viewed 2 times 0 $\begingroup$ I know, min. So we just have to find the point where the total derivative is 0. Click hereto get an answer to your question ️ If, in a triangle ABC,cosA + cosB + cosC = 7/4 , then R/r is equal to This question was voluntarily removed by its author. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Find the Maximum Values of cosA * cosB * cosc. are solved by group of students and teacher of JEE, which is also the largest student We will discuss every single trigonometry formulas from class 10 , 11 , 12 level upto college level. Thus the maximum value of cosA cosB cosC is 1/8 :) 2 1. given, cosA + cosB + cosC = 3/2 => 2(2cos(A + B)/2 . You can study other questions, MCQs, videos and tests for JEE on EduRev and even discuss your questions like FORMULA SHEET MATH 1060-004 Trigonometry The following formulas will be provided on the Final Test. If a + b + c = 180 degree prove that cos square A + cos square B + cos square C + 2 cos A ×cosB× cosC= 1Given A+B+C= 180 Taking LHS, Cos^2A+cos^2 B + cos^2 C+ 2 Of course, A and B aren't dependent on each other, so we can just set the two partials equal to zero to find the critical point(s): Note: we can divide by sin(A) because A≠0. rev 2021.1.8.38287, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Minimum height of mirror required to view image. This value exists for a degenerate . site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. 1) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. C: the variation of the rate as a function of temperature, obtained by subtracting from the rate at 8°C from that at 38°C, the whole divided … In a triangle ABC if cos A + cos B + cos C = 3/2, then the triangle is. 0 c. -2 d. none of these Q.4 The value of cosec10 3sec10 is equal to a. I can start with the fact that C = 180- A - B, and: cos A + cos B + cos C = cos A + cos B - (cos(A+B)) Now - for a given value of A, let's find the max for this function: 4 10 c. 0 d. none of these Q.6 If,x 9 tan and,x 18 5 tan are in AP and, y 9 tan and 18 7 tan Stack Exchange Network. is done on EduRev Study Group by JEE Students. Find the Maximum Values of cosA * cosB * cosc. 1 Answer +1 vote . If A+B+C=π then prove that Cos^A+Cos^B+Cos^C=1-2CosA.CosB.CosC plzz explain how to solve it with the solution Pls answer the attached questions ASAP 9 years ago. The Questions and Answers of The value of cosA + cosB + cosC in a triangle is less than 3/2 . Asked … Ask Question Asked today. Why can the “arrow” vectors be slid parallelly anywhere in space? Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The Questions and Answers of The value of cosA + cosB + cosC in a triangle is less than 3/2. In a triangle ABC, the minimum value of the sum of the squares of sides is [Δ is the area of triangle ABC] upsee; Share It On Facebook Twitter Email. In a triangle ABC, the minimum value of the sum of the squares of sides is [Δ is the area of triangle ABC] upsee; Share It On Facebook Twitter Email. sin(3x) has a minimum value of (-1) 4sin(3x) has a minimum value of -4. Sử dụng kết quả bất đẳng thức Bunyakovsky, chứng minh cosA+cosB+cosC \(\le\dfrac{3}{2}\) (A, B, C là các đỉnh của tam giác ABC). Is minimum value of CosA +CosB +CosC -3/2 here. math. 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