sintA tsint B t sent c +Cl-siuA)9.If ABC is an acute angled triangle then the minimum value ofsin A + (1sin A) + sin B + (1 - sin B)4 + sin C + (1- sin Cya is equal to :sintA tsint B+ sent c +C-siuA)"(A)16+ (r sinBt+Cl-sinc)(B)=ltsinA-2(C)(D) None of theseAns.(D)310

Claim: for 0≤x≤1, f(x) = x⁴+(1-x)⁴ is minimum when x = 1/2 Proof: f(x) = x⁴+(1-x)⁴ So, f'(x) = 4x³…

9. If ABC is an acute angled triangle then the minimum value of sin A + (1 -sin A)* + sin B + (1- sin B) + sin C+ (1-sin C) is equal to: sintA tsint B+sentc tcrsiuA)? 3 (A) 16 3 (B) 4. t Cr sinBt+ Cl-sinc) 一4 =ltsin'A-25 (D) None of these Ans. (D)

9. If ABC is an acute angled triangle then the minimum value of sin A + (1 -sin A)* + sin B + (1- sin B) + sin C+ (1-sin C) is equal to: sintA tsint B+sentc tcrsiuA)? 3 (A) 16 3 (B) 4. t Cr sinBt+ Cl-sinc) 一4 =ltsin'A-25 (D) None of these Ans. (D)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.2: Angles And Their Relationships

Problem 37E: Draw a triangle with three acute angles. Construct angle bisectors for each of the three angles. On...

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Question

sintA tsint B t sent c +Cl-siuA)
9.
If ABC is an acute angled triangle then the minimum value of
sin A + (1
sin A) + sin B + (1 - sin B)4 + sin C + (1- sin Cya is equal to :
sintA tsint B+ sent c +C-siuA)"
(A)
16
+ (r sinBt+Cl-sinc)
(B)
=ltsinA-2
(C)
(D) None of these
Ans.
(D)
310

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Draw a triangle with three acute angles. Construct angle bisectors for each of the three angles. On the basis of the appearance of your construction, what seems to be true?

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