nAnBnC⎧-4sinsinsin n=4k⎪222⎪⎪4cosnAcosnBcosnC n=4k+1⎪222*(1)sin(nA)+sin(nB)+sin(nC)=⎨，k∈N
⎪4sinnAsinnBsinnC n=4k+2⎪222⎪nAnBnC⎪-4coscoscos n=4k+3222⎩
(2)若A+B+C=π，则： sin2A+sin2B+sin2CABC=8sinsinsin sinA+sinB+sinC222
ABC②cosA+cosB+cosC=1+4sinsinsin 222
BCABC2A+sin2+sin2=1-2sinsinsin ③sin222222
ABCπ-Aπ-Bπ-Csinsin④sin+sin+sin=1+4sin 222444
ABC⑤sinA+sinB+sinC=4sinsinsin 222
ABCABC=cotcotcot ⑥cot+cot+cot222222
ABBCCA⑦tantan+tantan+tantan=1 222222①
⑧sin(B+C-A)+sin(C+A-B)+sin(A+B-C)=4sinAsinBsinC
(3)在任意△ABC中，有： ①sinABC1⋅sin⋅sin≤ 2228⑥cosA⋅cosB⋅cosC≤1 8⑫tan
⑬cotABC ⋅tan⋅tan≤2229ABC+cot+cot≥3 222②cos
③sinABC33 ⋅cos⋅cos≤2228ABC3+sin+sin≤ 2222⑦sinA+sinB+sinC≤3 2
④cosABC33 +cos+cos≤2222
3 8⑤sinA⋅sinB⋅sinC≤3 2BC32A+sin2+sin2≥ ⑨sin2224BC2A+tan2+tan2≥1 ⑩tan222ABC⑪tan+tan+tan≥ 222⑧cosA+cosB+cosC≤
22⑭cotA+cotB+cotC≥ (4)在任意锐角△ABC中，有： ①tanA⋅tanB⋅tanC≥3 ③tanA+tanB+tanC≥9
④cotA+cotB+cotC≥1 2222②cotA⋅cotB⋅cotC≤ 9
4 31.帕斯卡定理：如果一个六边形内接于一条二次曲线(椭圆、双曲线、抛物线)，那么它的三对对边的交点在同
nAnBnC⎧-4sinsinsin n=4k⎪222⎪⎪4cosnAcosnBcosnC n=4k+1⎪222*(1)sin(nA)+sin(nB)+sin(nC)=⎨，k∈N
⎪4sinnAsinnBsinnC n=4k+2⎪222⎪nAnBnC⎪-4coscoscos n=4k+3222⎩
(2)若A+B+C=π，则： sin2A+sin2B+sin2CABC=8sinsinsin sinA+sinB+sinC222
ABC②cosA+cosB+cosC=1+4sinsinsin 222
BCABC2A+sin2+sin2=1-2sinsinsin ③sin222222
ABCπ-Aπ-Bπ-Csinsin④sin+sin+sin=1+4sin 222444
ABC⑤sinA+sinB+sinC=4sinsinsin 222
ABCABC=cotcotcot ⑥cot+cot+cot222222
ABBCCA⑦tantan+tantan+tantan=1 222222①
⑧sin(B+C-A)+sin(C+A-B)+sin(A+B-C)=4sinAsinBsinC
(3)在任意△ABC中，有： ①sinABC1⋅sin⋅sin≤ 2228⑥cosA⋅cosB⋅cosC≤1 8⑫tan
⑬cotABC ⋅tan⋅tan≤2229ABC+cot+cot≥3 222②cos
③sinABC33 ⋅cos⋅cos≤2228ABC3+sin+sin≤ 2222⑦sinA+sinB+sinC≤3 2
④cosABC33 +cos+cos≤2222
3 8⑤sinA⋅sinB⋅sinC≤3 2BC32A+sin2+sin2≥ ⑨sin2224BC2A+tan2+tan2≥1 ⑩tan222ABC⑪tan+tan+tan≥ 222⑧cosA+cosB+cosC≤
22⑭cotA+cotB+cotC≥ (4)在任意锐角△ABC中，有： ①tanA⋅tanB⋅tanC≥3 ③tanA+tanB+tanC≥9
④cotA+cotB+cotC≥1 2222②cotA⋅cotB⋅cotC≤ 9
4 31.帕斯卡定理：如果一个六边形内接于一条二次曲线(椭圆、双曲线、抛物线)，那么它的三对对边的交点在同