在三角形ABC中,有4sinBsin²(π/√4 + B/2)+cos2B=1+√3在△ABC中,a,b,c分别为角A,B,C的对边,S为△ABC的面积,且有4sinBsin²(π/√4 + B/2)+cos2B=1+√31.求角B的度数;2.若a=4,S=5√3,求b的值
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![在三角形ABC中,有4sinBsin²(π/√4 + B/2)+cos2B=1+√3在△ABC中,a,b,c分别为角A,B,C的对边,S为△ABC的面积,且有4sinBsin²(π/√4 + B/2)+cos2B=1+√31.求角B的度数;2.若a=4,S=5√3,求b的值](/uploads/image/z/3717543-39-3.jpg?t=%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2C%E6%9C%894sinBsin%26%23178%3B%EF%BC%88%CF%80%2F%E2%88%9A4+%2B+B%2F2%EF%BC%89%2Bcos2B%3D1%2B%E2%88%9A3%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2Ca%2Cb%2Cc%E5%88%86%E5%88%AB%E4%B8%BA%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%2CS%E4%B8%BA%E2%96%B3ABC%E7%9A%84%E9%9D%A2%E7%A7%AF%2C%E4%B8%94%E6%9C%894sinBsin%26%23178%3B%EF%BC%88%CF%80%2F%E2%88%9A4+%2B+B%2F2%EF%BC%89%2Bcos2B%3D1%2B%E2%88%9A31.%E6%B1%82%E8%A7%92B%E7%9A%84%E5%BA%A6%E6%95%B0%EF%BC%9B2.%E8%8B%A5a%3D4%2CS%3D5%E2%88%9A3%2C%E6%B1%82b%E7%9A%84%E5%80%BC)
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在三角形ABC中,有4sinBsin²(π/√4 + B/2)+cos2B=1+√3在△ABC中,a,b,c分别为角A,B,C的对边,S为△ABC的面积,且有4sinBsin²(π/√4 + B/2)+cos2B=1+√31.求角B的度数;2.若a=4,S=5√3,求b的值
在三角形ABC中,有4sinBsin²(π/√4 + B/2)+cos2B=1+√3
在△ABC中,a,b,c分别为角A,B,C的对边,S为△ABC的面积,且有4sinBsin²(π/√4 + B/2)+cos2B=1+√3
1.求角B的度数;
2.若a=4,S=5√3,求b的值
在三角形ABC中,有4sinBsin²(π/√4 + B/2)+cos2B=1+√3在△ABC中,a,b,c分别为角A,B,C的对边,S为△ABC的面积,且有4sinBsin²(π/√4 + B/2)+cos2B=1+√31.求角B的度数;2.若a=4,S=5√3,求b的值
(1)
4sinBsin²(π/√4 + B/2)+cos2B=1+√3
2sinB(1-cos(π/2 + B)+cos2B=1+√3
2sinB(1+sinB)+cos2B=1+√3
2sinB+2sin²B+1-2sin²B=1+√3
2sinB=√3
sinB=√3/2,
B=60°或B=120°
(2)1/2 *acsinB=5√3
1/2 *4*c*√3/2=5√3
解得:c=5
b²=a²+c²-2accosB=41-40cosB
B=60° b²=21,b=√21
B=120°b²=81,b=9