sin(2x)/1+cos(2x)=3/4,求tan(x/2)的数学题
问题描述：
sin(2x)/1+cos(2x)=3/4,求tan(x/2)的数学题
答
哎!都忘光了
答
sin(2x)/1+cos(2x)=3/4
=tanx
tanx=2tan(x/2)/(1-tan(x/2)^2)=3/4
2tan(x/2)=3/4-3/4tan(x/2)^2
8tan(x/2)=3-3tan(x/2)^2
3tan(x/2)^2+8tan(x/2)-3=0
tan(x/2)=-3或1/3
答
2sinxcosx/2cos^2x=3/4tanx=3/4tan2A=2tanA/（1-tanA^2）3/4=2tan(x/2)/(1-tan^2(x/2))3-3tan^2(x/2)=8tan(x/2)3tan^2(x/2)+8tan(x/2)-3=0(3tan(x/2)-1)(tan(x/2)+3)=0tan(x/2)=1/2tan(x/2)=-3