Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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
7 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
7 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 ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free