Question

cos A + cos B + cos C where A B and C are the angles of any triangle

Answer 1

Kehna kia chate ho ?

Answer 2

do we have options/choices for this ?

Answer 3

iwant to simplify it...

Answer 4

\[\frac{ 1 }{ \sec A }+\frac{ 1 }{ \sec B }+\frac{ 1 }{ \sec C }\]

Answer 5

\(\large = 1 + 4\sin{\frac{A}{2}}\sin\frac{B}{2}\sin\frac{C}{2}\)

Answer 6

cos A + cos B + cos C
is in the most simplified form

Answer 7

Yeah right :)

Answer 8

in 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.

Answer 9

Well 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

Answer 10

I did like this :

\[\large{\frac{(b^2+c^2-a^2)}{2bc} + \frac{(c^2+a^2-b^2)}{2ac} + \frac{(a^2+b^2-c^2)}{2ab}}\]
and simpified this by taking LCM and taking terms common and I got :

\[\large{\frac{-4s^3}{abc}}\]

Answer 11

you mean u got
\(ab^2+ac^2+ba^2+bc^2+ca^2+cb^2-a^3-b^3-c^3=-8s^3\)

Answer 12

let me show you my complete work wait..

Answer 13

that doesn't hold for an equilateral triangle, all sides equal, say =1

Answer 14

Yes but I am getting this answer by simplifying cos A + cos B + cos C by using cosines law..

Answer 15

ok, show your work, we'll find the error...

Answer 16

ok 1 minute

Answer 17

Oh! I think I got my mistake ... ..

Answer 18

can you help me to prove that cos A + cos B + cos C is less than or equal to 2

Answer 19

I got some conceptual answers previous time but I am searching for a numerical one..

@hartnn

Answer 20

And mine was numerical but only for a right triangle =/

Answer 21

=/ yeah @hartnn any try?

Answer 22

if i get something, i'll post.

Answer 23

\[{cos A + cos B + cos C = \\ \frac{a(b^2+c^2) + b(a^2+c^2) + \\c(a^2+b^2) - (a+b+c)(a^2+b^2+c^2-ab-bc-ca)}{2abc}}\]

Answer 24

trying on paper

Answer 25

Thanks! I am also trying my best...

Answer 26

got it !

Answer 27

?