在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a.b.c成等差数列,求角B的取值范围.在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a、b、c成等差数列,求角B的取值范围.
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![在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a.b.c成等差数列,求角B的取值范围.在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a、b、c成等差数列,求角B的取值范围.](/uploads/image/z/7215141-21-1.jpg?t=%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2Cacos%5E2%2AC%2F2%2Bccos%5E2%2AA%2F2%3D3b%2F2%2C%E5%B7%B2%E6%B1%82%E5%BE%97a.b.c%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E6%B1%82%E8%A7%92B%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2Cacos%5E2%2AC%2F2%2Bccos%5E2%2AA%2F2%3D3b%2F2%2C%E5%B7%B2%E6%B1%82%E5%BE%97a%E3%80%81b%E3%80%81c%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E6%B1%82%E8%A7%92B%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a.b.c成等差数列,求角B的取值范围.在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a、b、c成等差数列,求角B的取值范围.
在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a.b.c成等差数列,求角B的取值范围.
在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a、b、c成等差数列,求角B的取值范围.
在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a.b.c成等差数列,求角B的取值范围.在三角形ABC中,acos^2*C/2+ccos^2*A/2=3b/2,已求得a、b、c成等差数列,求角B的取值范围.
(1)
acos^C/2+ccos^A/2=3/2b
LZ的意思应该是a(cos(C/2))^2+c(cos(A/2))^2=3/2b吧~
a(cos(C/2))^2+c(cos(A/2))^2
=a*(1+cosC)/2+c(1+cosA)/2
=a/2+c/2+(acosC+ccosA)/2
=a/2+c/2+b/2 (做高BH,则acosC+ccosA=AH+CH=AC=b)
=3/2*b
a+c=2b
故a,b,c成等差数列
cosB=(a^2+c^2-b^2)/(2*a*c)
=(a^2+c^2-((a+c)/2)^2)/(2*a*c)
=(3*a^2+3*c^2-2*a*c)/(8*a*c)
=(3*a^2+3*c^2-6*a*c)/(8*a*c)+1/2
=3*(a-c)^2/(8*a*c)+1/2
>=1/2
所以 0
(1)
acos^C/2+ccos^A/2=3/2b
a(cos(C/2))^2+c(cos(A/2))^2
=a*(1+cosC)/2+c(1+cosA)/2
=a/2+c/2+(acosC+ccosA)/2
=a/2+c/2+b/2 (做高BH,则acosC+ccosA=AH+CH=AC=b)
=3/2*b
a+c=2b
故...
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(1)
acos^C/2+ccos^A/2=3/2b
a(cos(C/2))^2+c(cos(A/2))^2
=a*(1+cosC)/2+c(1+cosA)/2
=a/2+c/2+(acosC+ccosA)/2
=a/2+c/2+b/2 (做高BH,则acosC+ccosA=AH+CH=AC=b)
=3/2*b
a+c=2b
故a,b,c成等差数列
cosB=(a^2+c^2-b^2)/(2*a*c)
=(a^2+c^2-((a+c)/2)^2)/(2*a*c)
=(3*a^2+3*c^2-2*a*c)/(8*a*c)
=(3*a^2+3*c^2-6*a*c)/(8*a*c)+1/2
=3*(a-c)^2/(8*a*c)+1/2
>=1/2
所以 0<角B<=60度
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