作业帮高中三角函数二倍角的正切、余切1.化简2sin2x/1+cos2x × cos^2x/cos2x = 2.cos^2 (x-π/4)=1/4 sin2x = 3.已知tanA+cotA=m ze sin2A = sin6度cos24度sin78度cos48度=
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/15 22:56:33
高中三角函数二倍角的正切、余切1.化简2sin2x/1+cos2x × cos^2x/cos2x = 2.cos^2 (x-π/4)=1/4 sin2x = 3.已知tanA+cotA=m ze sin2A = sin6度cos24度sin78度cos48度=
高中三角函数二倍角的正切、余切
1.化简2sin2x/1+cos2x × cos^2x/cos2x =
2.cos^2 (x-π/4)=1/4 sin2x =
3.已知tanA+cotA=m ze sin2A =
sin6度cos24度sin78度cos48度=
高中三角函数二倍角的正切、余切1.化简2sin2x/1+cos2x × cos^2x/cos2x = 2.cos^2 (x-π/4)=1/4 sin2x = 3.已知tanA+cotA=m ze sin2A = sin6度cos24度sin78度cos48度=
1、
=[2sin2x/(1+2cos²x-1)](cos²x/cos2x)
=(2sin2x/2cos²x)(cos²x/cos2x)
=sin2x/cos2x
=tan2x
2、
sin2x=cos(π/2-2x)
=cos[2(π/4-x)]
=2cos²(π/4-x)-1
=2cos²(x-π/4)-1
=-7/8
3、
tanA+cotA
=sinA/cosA+cosA/sinA
=(sin²A+cos²A)/(sinAcosA)
=1/(sinAcosA)
=2/(2sinAcosA)
=2/sin2A
=m
sin2A=2/m
4、
原式=sin6cos24cos(90-78)cos48
=sin6cos12cos24cos48
=2sin6cos6cos12cos24cos48/(2cos6)
=sin12cos12cos24cos48/(2cos6)
=2sin12cos12cos24cos48/(4cos6)
=sin24cos24cos48/(4cos6)
=2sin24cos24cos48/(8cos6)
=sin48cos48/(8cos6)
=2sin48cos48/(16cos6)
=sin96/(16cos6)
=sin(90+6)/(16cos6)
=cos6/(16cos6)
=1/16
1.
=4sin(x)cos(x)/2cos^2(x) * cos^2(x)/cos(2x)
=2sin(x)cos(x)/cos(2x)
=tan(2x)
2.
cos[2(x-pi/4)]=2cos^2(x-pi/4)-1=-1/2
cos(2x-pi/2)=-1/2
sin(2x)=-1/2
3.
sinA/cosA+cosA/sinA=m
sin^2A+cos^2A/[sinAcosA]=m
sinAcosA=1/m
sin2A=2/m
*代表乘号，/表示除以号，p代表圆周率
1+cos2a=2*cosa*cosa, cosa*cosa=[1+cos2a]/2 【A】
1】2sin2x/[1+cos2x] *cosx*cosx/cos2x =2sin2x/[2cosx*cosx]*cosx*cosx/cos2x
=2sin2x/[2*cos2x*cos2x]*cosx*cosx/cos2x=sin2x/co...
全部展开
*代表乘号，/表示除以号，p代表圆周率
1+cos2a=2*cosa*cosa, cosa*cosa=[1+cos2a]/2 【A】
1】2sin2x/[1+cos2x] *cosx*cosx/cos2x =2sin2x/[2cosx*cosx]*cosx*cosx/cos2x
=2sin2x/[2*cos2x*cos2x]*cosx*cosx/cos2x=sin2x/cos2x=tan2x
2】cos(x-P/4)*cos(x-p/4)=1/4
根据【A】式得[1+cos(2x-p/2)]/2=1/4
cos(2x-p/2)=-1/2 cos[p/2-2x]=-1/2 即 sin2x=-1/2
收起