已知△ABC中,满足三内角sin^B+sin^2C-sinBsinC=sin^2A,则A=?
问题描述：
已知△ABC中,满足三内角sin^B+sin^2C-sinBsinC=sin^2A,则A=?
还有一题啊,函数y=sinxcosxcos2x的值域为?
答
(1)
sin^2B+sin^2C-sinBsinC=sin^2A
先用正弦定理得
b^2+c^2-bc=a^2
再用余弦定理得
cosA=(b^2+c^2-a^2)/(2bc)=bc/(2bc)=1/2
∴A=30°
(2)
y=sinxcosxcos2x
=1/2*2sinxcosxcos2x
=1/2*sin2x*cos2x
=1/4*2sin2x*cos2x
=1/4sin4x
值域是[-1/4,1/4]