Observe the following lists Match the following inequalities in an acute-angled triangle (equality should be attained):
Column-I | Column-II |
(i) cos A + cos B + cos C | [A] ≥ 1 |
(ii) tan A + tan B + tan C | [B] ≥ 3 |
(iii) sin A + sin B + sin C | [C] ≤ |
(iv) tan2 + tan2 + tan2 | [D] ≤ |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) - [A] , [D]
(ii) - [B]
(iii)- [C]
(iv)- [A]
Sol. (i) By symmetric function rule max
(cos A + cos B + cos C) = 
and min (cos A + cos B + cos C) = 1
using cos A + cos B + cos C = 1 + 4 sin 
sin 
sin 
(ii) Again by same rule tan A + tan B + tan C ≥ 3 
(tan function ∴ minimum)
(iii) Similarly (iii) → C and tan 2 
+ tan 2 
+ tan 2 
≥ tan 
tan 
tan 
+ tan 
tan 
= 1
(iv) >1
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