If A,B,C are angles of a triangle,
then prove that cosA+cosB+cosC<3/2
Sandeep Sourav , 12 Years ago
Grade 11
Trigonometry> identities...
2 AnswersNirmal Singh.
let angle a= 30 degree
angle b = 90 degree
angle c = 60 degree
angle b = 90 degree
angle c = 60 degree
- now
=sqrt 3/2 + 0 + 1/2
= ( sqrt 3+1 )/2
now we can compare the value of cos a + cos b + cos c and 3/2
cosA+cosB+cosC<3/2
proved
= ( sqrt 3+1 )/2
now we can compare the value of cos a + cos b + cos c and 3/2
cosA+cosB+cosC<3/2
proved
rajusharma
from JENSEN`S inequality-
f(a)+f(b)+f(c)<3f(a+b+c/3)
if f(x)=cosx
then f(A)=cosA
f(B)=cosB
f(C)=cosC
and A+B+C=Pi
now
f(A)+f(B)+f(C)<3f(A+B+C/3)
cosA+cosB+cosC<3cos(pi/3)
cosA+cosB+cosC<3/2
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