cos2B-cos2A=2sin(π/3+B)sin(π/3-B).设△ABC的内角A,B,C的对应边分别为a,b,c.已知角A.cos2B-cos2A=2sin(π/3+B)sin(π/3-B).(1)求角A的大小.(2)试确定满足条件a=2√2,b=3的△ABC的个数.
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![cos2B-cos2A=2sin(π/3+B)sin(π/3-B).设△ABC的内角A,B,C的对应边分别为a,b,c.已知角A.cos2B-cos2A=2sin(π/3+B)sin(π/3-B).(1)求角A的大小.(2)试确定满足条件a=2√2,b=3的△ABC的个数.](/uploads/image/z/1606721-41-1.jpg?t=cos2B-cos2A%3D2sin%28%CF%80%2F3%2BB%29sin%28%CF%80%2F3-B%29.%E8%AE%BE%E2%96%B3ABC%E7%9A%84%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E5%BA%94%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc.%E5%B7%B2%E7%9F%A5%E8%A7%92A.cos2B-cos2A%3D2sin%28%CF%80%2F3%2BB%29sin%28%CF%80%2F3-B%29.%281%29%E6%B1%82%E8%A7%92A%E7%9A%84%E5%A4%A7%E5%B0%8F.%282%29%E8%AF%95%E7%A1%AE%E5%AE%9A%E6%BB%A1%E8%B6%B3%E6%9D%A1%E4%BB%B6a%3D2%E2%88%9A2%2Cb%3D3%E7%9A%84%E2%96%B3ABC%E7%9A%84%E4%B8%AA%E6%95%B0.)
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cos2B-cos2A=2sin(π/3+B)sin(π/3-B).设△ABC的内角A,B,C的对应边分别为a,b,c.已知角A.cos2B-cos2A=2sin(π/3+B)sin(π/3-B).(1)求角A的大小.(2)试确定满足条件a=2√2,b=3的△ABC的个数.
cos2B-cos2A=2sin(π/3+B)sin(π/3-B).
设△ABC的内角A,B,C的对应边分别为a,b,c.已知角A.cos2B-cos2A=2sin(π/3+B)sin(π/3-B).(1)求角A的大小.
(2)试确定满足条件a=2√2,b=3的△ABC的个数.
cos2B-cos2A=2sin(π/3+B)sin(π/3-B).设△ABC的内角A,B,C的对应边分别为a,b,c.已知角A.cos2B-cos2A=2sin(π/3+B)sin(π/3-B).(1)求角A的大小.(2)试确定满足条件a=2√2,b=3的△ABC的个数.
(1)展开化简得:2cos^2B-1-cos2A=2[3cos^2B-sin^2B]/4 ===>4cos^2B-2-2cos2A=4cos^2B-1
cos2A=-1/2,2A=120°,A=60°
(2)2√2/sin60°=3/sinB b>a,B>A,sinB=(3根号6】/8
1)等式右边用积化和差可得= cos2B+1/2.则易得A=2p/3或p/3
2)因为a
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