Cho $\Delta ABC$. Chứng minh rằng:
$\cos \frac{A}{2}+ \cos \frac{B}{2}+ \cos \frac{C}{2}\geq \sqrt{\frac{3}{2}}\left ( \sqrt{\sin \frac{A}{2}}+ \sqrt{ \sin \frac{B}{2}}+ \sqrt{\sin \frac{C}{2}} \right )$
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#2
Posted 05-01-2018 - 16:17
moriran
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- Pre-Member
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- 24 posts
Binh nhất
Cho $\Delta ABC$. Chứng minh rằng:
$\cos \frac{A}{2}+ \cos \frac{B}{2}+ \cos \frac{C}{2}\geq \sqrt{\frac{3}{2}}\left ( \sqrt{\sin \frac{A}{2}}+ \sqrt{ \sin \frac{B}{2}}+ \sqrt{\sin \frac{C}{2}} \right )$
#3
Posted 05-01-2018 - 18:17
Zaraki
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- Phó Quản lý Toán Cao cấp
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- 4273 posts
PQT
Bài trên THTT chưa hết hạn. Khóa topic.
Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.
Grothendieck, Récoltes et Semailles (“Crops and Seeds”).
Also tagged with one or more of these keywords: bất đẳng thức lượng giác
 
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Toán thi Học sinh giỏi và Olympic →
Bất đẳng thức - Cực trị →
Cho tam giác ABC nhọn...Started by dai101001000, 05-01-2018  bất đẳng thức lượng giác
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Toán thi Học sinh giỏi và Olympic →
Hình học →
Cho tam giác ABC nhọn...Started by dai101001000, 05-01-2018 bất đẳng thức lượng giác
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Toán thi Học sinh giỏi và Olympic →
Bất đẳng thức - Cực trị →
cos〖A/2〗+ cos〖B/2〗+ cos〖C/2〗≥ √(3/2) (√(sin〖A/2〗 )+√(sin〖B/2〗 )+ √(sin〖C/2〗 ))Started by INXANG, 05-01-2018 bất đẳng thức lượng giác
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