Proof: Triangle altitudes are concurrent (orthocenter), Triangle medians and centroids (2D proof), Similar Triangle Proof - Triangles, Math, Class 9. 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. The Questions and Answers of The value of cosA + cosB + cosC in a triangle is less than 3/2 . If A+B=C, Prove that cos^2A+cos^2B+cos^2C=1+2cosA.cosB.cosC? Active today. over here on EduRev! asked May 2, 2019 in Mathematics by Niharika (75.6k points) asked May 2, 2019 in Mathematics by Niharika (75.6k points) math. are solved by group of students and teacher of JEE, which is also the largest student community of JEE. Why can the “arrow” vectors be slid parallelly anywhere in space? If the answer is not available please wait for a while and a community member will probably answer this Proof? 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 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. is done on EduRev Study Group by JEE Students. EduRev is a knowledge-sharing community that depends on everyone being able to pitch in when they know something. I know, min. 9 years ago. 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). 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. Is translation of position vectors allowed. given, cosA + cosB + cosC = 3/2 => 2(2cos(A + B)/2 . Learn in our Free Webinar. are solved by group of students and teacher of JEE, which is also the largest student Here are some similar questions that might be relevant: If you feel something is missing that should be here, contact us. Pre-Calc. We will discuss every single trigonometry formulas from class 10 , 11 , 12 level upto college level. Why perpendicular vectors do not share components? In a triangle ABC if cos A + cos B + cos C = 3/2, then the triangle is. By continuing, I agree that I am at least 13 years old and have read and Is minimum value of CosA +CosB +CosC -3/2 here. 4 10 b. This value exists for a degenerate . 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. 1 Answer +1 vote . Question bank for JEE. soon. 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. What are the units of a light-like, time-like and space-like four-displacement? 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. 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 . 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 $1$. 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. If the answer is not available please wait for a while and a community member will probably answer this soon. This question was voluntarily removed by its author. Click hereto get an answer to your question ️ If, in a triangle ABC,cosA + cosB + cosC = 7/4 , then R/r is equal to Find the Maximum Values of cosA * cosB * cosc / Home / Questions / Categories / Aptitude Questions / Arithmetic Aptitude. = -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) 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. 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