0

Guest

Courses New

If A,B,C are angles of a triangle, then prove that cosA+cosB+cosC<3/2

If A,B,C are angles of a triangle,
then prove that cosA+cosB+cosC<3/2

Grade:11

2 Answers

Nirmal Singh.
askIITians Faculty 44 Points
10 years ago
let angle a= 30 degree
angle b = 90 degree
angle c = 60 degree
  • now
cos a + cos b + cos c = cos 30+cos90+cos60
=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
rajusharma
12 Points
10 years ago
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

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More