ddng.net
当前位置:首页 >> tAnx/2= =sinx/(1+Cosx) =(1%Cosx)/sinx。 怎么推 >>

tAnx/2= =sinx/(1+Cosx) =(1%Cosx)/sinx。 怎么推

把2倍角公式带进去就行了,第一个代入下面第一、二两个,第二个代入下面第一、三两个.sinx = 2sin(x/2)*cos(x/2) cosx = 2cos(x/2)*cos(x/2) - 1 cosx = 1 - 2sin(x/2)*sin(x/2)

证明:tan(x/2)=sin(x/2)/cos(x/2)=2sin(x/2)cos(x/2)/[cos(x/2)]^2=sinx/(1+cosx)=sinx(1-cosx)/[1-(cosx)^2]=sinx(1-cosx)/(sinx)^2=(1-cosx)/sinx

tanx/2=sin(x/2)/cos(x/2)=(2sin(x/2)cos(x/2))/2(cos^2(x/2))=sinx/(1+cosx)tanx/2=sin(x/2)/cos(x/2)=2(sin^2(x/2))/(2sin(x/2)cos(x/2))=(1-cosx)/sinx运用到的公式有sinx=2sin(x/2)cos(x/2)cosx=1-2sin^2(x/2)=1+2cos^2(x/2)

tanx/2=(sinx/2)/cos(x/2)上下同乘以2sinx/2上面变成1-cosx 因为cosx=1-2(sinx/2)^2 1-cosx=2(sinx/2)^2下面变成sinx (因为sinx=2sinx/2 * cosx/2 )

tanx=(2tan(x/2))/(1-(tan(x/2))2)1=(tan(x/2))2+(2tan(x/2))/tanx(tan(x/2)+1/tanx)2=1+1/(tanx)2因为1+1/(tanx)2=((tanx)2+1)/(tanx)2=1/(sinx)2所以tan(x/2)+1/tanx=1/sinxtan(x/2)=1/sinx-cosx/sinx=(1-cosx)/sinx(sinx)2=(1+cosx)*(1-cosx) 1-cosx=(sinx)2/(1+

sinx=2sin(x/2)*cos(x/2)cosx+1=[cos(x/2)]^2-[sin(x/2)]^2 +[cos(x/2)]^2-[sin(x/2)]^2 =2[cos(x/2)]^2∴sinx/(1+cosx)= 2sin(x/2)*cos(x/2)/2[cos(x/2)]^2=tanx/2得证!

tan(x/2)=[sin(x/2)]/[cos(x/2)]上下同乘以2cos(x/2)=[2cos(x/2)sin(x/2)]/[2cos(x/2)cos(x/2)]由2倍角公式=sinx/(1+cosx)

sinx/(1+cosx)=2sin(x/2)cos(x/2)/2cos(x/2)cos(x/2)=tan(x/2)(1-cosx)/sinx=2sin(x/2)sin(x/2)/2sin(x/2)cos(x/2)=tan(x/2) 所以tan(x/2)= sinx/(1+cosx)=(1-cosx)/sinx

你的公式写错了把 按你这tan样推论 tan=2(1- (sinx/cosx)) 得出的2-2tanx=tanx 2=3tanx 不成立吧 是不是这样的 tanx/2=(1-sinx)/cosx

tanx=sinx/cosx一个式子分子分母同时除以 cosx得到 ,(sinX十COSx)/(sinX一cOsX) =(tanx+1)/(tanx-1)=(2+1)/(2-1)=3

相关文档
网站首页 | 网站地图
All rights reserved Powered by www.ddng.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com