已知△ABC满足b²=√3bc+a²-c².求:1)∠A的大小.2)sin(C-B)+2sinBcosC的值
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已知△ABC满足b²=√3bc+a²-c².求:1)∠A的大小.2)sin(C-B)+2sinBcosC的值
已知△ABC满足b²=√3bc+a²-c².求:1)∠A的大小.2)sin(C-B)+2sinBcosC的值
已知△ABC满足b²=√3bc+a²-c².求:1)∠A的大小.2)sin(C-B)+2sinBcosC的值
(1)因为b^2=√3bc+a^2-c^2
所以√3/2=(b^2+c^2-a^2)/2bc
由余弦定理得cosA=√3/2
所以A=30°
(2)sin(C-B)+2sinBcosC
=sinCcosB-cosCsinB+2sinBcosC
=sinCcosB+cosCsinB
=sin(B+C)=sin[π-(B+C)]
=sinA
=1/2
b²=√3bc+a²-c²
b²+c²-a²=√3bc
cosA=(b²+c²-a²)/2bc=√3/2
A=π/6
sin(C-B)+2sinBcosC
=sinCcosB-cosCsinB+2sinBcosC
=sinCcosB+cosCsinB
=sin(C+B)=sinA=1/2
原式变为b^2+c^2-a^2=根号3 bc
所以cosA=根3/2∴∠A=60
a^2=b^2+c^2-√3bc
a^2=b^2+c^2-2bccosA
2cosA=√3
A=30
sin(C-B)+2sinBcosC=sin(C-B)+sin(B+C)+sin(B-C)=sin(B+C)=sinA=1/2
(1)因为b^2=√3bc+a^2-c^2
所以√3/2=(b^2+c^2-a^2)/2bc
由余弦定理得cosA=√3/2
所以A=30°
(2)sin(C-B)+2sinBcosC
=sinCcosB-cosCsinB+2sinBcosC
=sinCcosB+cosCsinB
=sin(B+C)=sin[π-(B+C)]
=sin...
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(1)因为b^2=√3bc+a^2-c^2
所以√3/2=(b^2+c^2-a^2)/2bc
由余弦定理得cosA=√3/2
所以A=30°
(2)sin(C-B)+2sinBcosC
=sinCcosB-cosCsinB+2sinBcosC
=sinCcosB+cosCsinB
=sin(B+C)=sin[π-(B+C)]
=sinA
=1/2
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