A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1do we have options/choices for this ?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0iwant to simplify it...

hba
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ \sec A }+\frac{ 1 }{ \sec B }+\frac{ 1 }{ \sec C }\]

FoolAroundMath
 2 years ago
Best ResponseYou've already chosen the best response.0\(\large = 1 + 4\sin{\frac{A}{2}}\sin\frac{B}{2}\sin\frac{C}{2}\)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1cos A + cos B + cos C is in the most simplified form

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1in any triangle , A+B+C = \(\pi\), so \(\cos(A+B)=\cos C\) \(\cos(C+B)=\cos A\) \(\cos(A+C)=\cos B\) if you want to complicate, i can help :P using cosine law.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Well yes I wanted to use cosine law here and I got : cos A + cos B + cos C = \(\LARGE{\frac{4s^3}{abc}}\) where a , b and c are the sides of the triangle and s is semi perimeter of the triangle

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0I did like this : \[\large{\frac{(b^2+c^2a^2)}{2bc} + \frac{(c^2+a^2b^2)}{2ac} + \frac{(a^2+b^2c^2)}{2ab}}\] and simpified this by taking LCM and taking terms common and I got : \[\large{\frac{4s^3}{abc}}\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1you mean u got \(ab^2+ac^2+ba^2+bc^2+ca^2+cb^2a^3b^3c^3=8s^3\)

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0let me show you my complete work wait..

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1that doesn't hold for an equilateral triangle, all sides equal, say =1

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Yes but I am getting this answer by simplifying cos A + cos B + cos C by using cosines law..

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1ok, show your work, we'll find the error...

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Oh! I think I got my mistake ... ..

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0can you help me to prove that cos A + cos B + cos C is less than or equal to 2

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0I got some conceptual answers previous time but I am searching for a numerical one.. @hartnn

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0And mine was numerical but only for a right triangle =/

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0=/ yeah @hartnn any try?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1if i get something, i'll post.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0\[{cos A + cos B + cos C = \\ \frac{a(b^2+c^2) + b(a^2+c^2) + \\c(a^2+b^2)  (a+b+c)(a^2+b^2+c^2abbcca)}{2abc}}\]

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks! I am also trying my best...

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2now cos A+cos B+Cos C is always less than equal to 3

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0We have to prove for less than or equal to 2

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2why not ?where u have doubt ?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0cos A + cos B  cos(A+B) , how is it less than or equal to 3 ?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2i wrote cos A+cos B+cos(18(A+B)<=3

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2this is because maximum value of cos is 1

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2all other cases cos a +cos b +cos c value will be less than 3

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2and note i wrote c as 180(A+B)

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2@mathslover you get it?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Are you taking A = B = 0 degrees?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0since cos A + cos B + cos (180(A+B)) = 3 is not possible ?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0I may be wrong but please correct me if I am ...

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2yep for maximum value we take A=B=C=0 degree

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0but A , B and C are the angles of a triangle..

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2yess that was in general case

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2in the triangle case angle c is replaced by 180(A+B)

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2hence cos C becomes cos (180(A+B))

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Yes but we can not take the angles of a triangle as 0 degrees..

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2i didnt told you to take !!i said that is general case!

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2but equal to not possible

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2in triangle you have equation cos A+cos B+cos(180(A+B))<3

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0so can cos A + cos B +cos C be greater than 2 also ?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2no ! thats where we apply trigonometry ! os(180x)=sin x

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2you understand that much?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0cos ( 180  x ) =  cos (x)

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2so our equation for triangle becomes cos A+cos Bcos(A+B)<3

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0got it now thanks a lot

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2:) you are welcome bro!

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1directly comes from,\(\cos(A+B)=\cos C\) than from cos A+cos Bcos(A+B)<3 how u proved cos A+cos B+cos C<=2

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2simple cos A +cos B maximum can be 2 and cos(a+b) is a reducing term so it always results in value less than or equal to 2 for the expression

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1ohh..in 1st and 4th Quadrant cos is positive....

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2ya whatever value cos takes it wont exceed +2

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1i thought cos(A+B) could be negative, thats why i doubted..but cos (A+B) will be positive...

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.2its all about the quadrants :)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.