Chương 1: Đẳng thức trong tAM GIÁC
tam giác ABC luôn có
1/ sinA+ sinB+ sinC=4cos$\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}$
2/sin2A+sin2B+sin2C=4sinAsinBsinC
3/ sin3A + sin3B + sin3C = -4$cos\frac{3A}{2}cos\frac{3B}{2}cos\frac{3C}{2}$
4/ sin 4A + sin 4B + sin 4C = -4sin 2A.sin 2B. sin 2C
5/ cos A + cos B + cos C =1+ 4$sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
6/
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9/
10/
11/ sin(2k+1)A + sin(2k+1)B + sin(2k+1)C =$(-1)^{k}.4cos(2k+1)\frac{A}{2}.cos(2k+1)\frac{B}{2}.cos(2k+1)\frac{C}{2} (k\epsilon Z)$
12/ sin2kA+ sin 2kB + sin 2kC= $(-1)^{k+1}.4sinkA.sinkB.sinkC$
13/ cos(2k+1)A + cos(2k+1)B + cos(2k+1)C =1+ $(-1)^{k}.4.sin(2k+1)\frac{A}{2}.sin(2k+1)\frac{B}{2}.sin(2k+1)\frac{C}{2}$
14/ cos2kA+cos2kB + cos2kC = -1 + $(-1)^{k}$.4coskA.coskB.coskC
15/ tankA + tankB + tankC =tankA.tankB.tankC
16/
17/cotgkA.cotgkB + cotgkB.cotgkC + cotgkC.cotgkA =1
18/
19/ $tan(2k+1)\frac{A}{2}.tan(2k+1)\frac{B}{2} + tan(2k+1)\frac{B}{2}.tan(2k+1)\frac{C}{2} + tan(2k+1)\frac{C}{2}.tan(2k+1)\frac{A}{2} =1$
20/
21/ $cotg(2k+1)\frac{A}{2}+ cotg(2k+1)\frac{B}{2} + cotg(2k+1)\frac{C}{2} =cotg(2k+1)\frac{A}{2}.cotg(2k+1)\frac{B}{2}.cotg(2k+1)\frac{c}{2}$
22/
23/
24/ $cos^{2}kA + cos^{2}kB + cos^{2}kC =1 +(-1)^{k}.2.coskA.coskB.coskC$
$sin^{2}kA + sin^{2}kB + sin^{2}kC = 2 +(-1)^{k+1}.2.coskA.coskB.coskC$
25/ $sin^{3}A.cos(B-C) + sin^{3}B.cos(C-A)+ sin^{3}C.cos(A-B)= 3sinAsinBsinc$
26/ $sin^{3}A.sin(B-C) + sin^{3}B.sin(C-A)+ sin^{3}C.sin(A-B)= 0$
27/ $sin3A.sin^{3}(B-C) + sin3B.sin^{3}(C-A)+ sin3C.sin^{3}(A-B)= 0$
28/ $sin3A.cos^{3}(B-C) + sin3B.cos^{3}(C-A)+ sin3C.cos^{3}(A-B)= sin3Asin3Bsin3C$
29/ $a=\frac{p.sin\frac{A}{2}}{cos\frac{B}{2}cos\frac{C}{2}}$
30/ bc=$\frac{(b+c)^{2}}{(b+c)^{2}-a^{2}}l$a$^{2}$
31/ $\frac{a^{2}-b^{2}}{c^{2}}=\frac{sin(A-B)}{sinC}$
32/ $(b+c)^{2} - 2(a^{2}+2l_{a}^2)(b+c)^{2} + a^{2}(a^{2}+ 4h_{a}^2) = 0$
$$33/ l_{a}=\frac{2bc}{b+c}.\cos \frac{A}{2}$
$34/ m_{a}^{2}+m_{b}^{2}+m_{c}^{2}=\frac{3}{4}(a^{2}+b^{2}+c^{2})$
$35/ (\frac{1}{a}+\frac{1}{b})l_{c} + (\frac{1}{b}+\frac{1}{c})l_{a}+ (\frac{1}{c}+\frac{1}{a})l_{b} = 2(cos\frac{A}{2}+cos\frac{B}{2}+cos\frac{C}{2})$$
36/ $r= p.tan\frac{A}{2}.tan\frac{B}{2}.tan\frac{C}{2}$
37/ $r= \frac{a.sin\frac{B}{2}sin\frac{C}{2}}{cos\frac{A}{2}}$
38/ $R= \frac{p}{4cos\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}}$
39/ $\frac{r}{4R}= sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
Bài viết đã được chỉnh sửa nội dung bởi xuanha: 23-10-2012 - 20:24
