求证:2sinx•cosx(sinx+cosx−1)(sinx−cosx+1)=1+cosxsinx
来源:学生作业帮 编辑:灵鹊做题网作业帮 分类:数学作业 时间:2024/04/26 03:33:20
求证:
=
2sinx•cosx |
(sinx+cosx−1)(sinx−cosx+1) |
1+cosx |
sinx |
左边=
2sinx•cosx
(sinx+cosx−1)(sinx−cosx+1)
=
2sinx•cosx
sin2x−(cosx−1)2
=
2sinx•cosx
sin2x−cos2x+2cosx−1
=
2sinx•cosx
−2cos2x+2cosx
=
sinx
1−cosx
=
sinx(1+cosx)
(1−cosx)(1+cosx)
=
sinx(1+cosx)
1−cos2x
=
1+cosx
sinx=右边.
∴
2sinx•cosx
(sinx+cosx−1)(sinx−cosx+1)=
1+cosx
sinx.
2sinx•cosx
(sinx+cosx−1)(sinx−cosx+1)
=
2sinx•cosx
sin2x−(cosx−1)2
=
2sinx•cosx
sin2x−cos2x+2cosx−1
=
2sinx•cosx
−2cos2x+2cosx
=
sinx
1−cosx
=
sinx(1+cosx)
(1−cosx)(1+cosx)
=
sinx(1+cosx)
1−cos2x
=
1+cosx
sinx=右边.
∴
2sinx•cosx
(sinx+cosx−1)(sinx−cosx+1)=
1+cosx
sinx.
求证:2sinx•cosx(sinx+cosx−1)(sinx−cosx+1)=1+cosxsinx
求证cosX/(1+sinx)-sinx/(1+cosx)=2(cosx-sinx)/(1+sinx+cosx)
3sinx-2cosx=0 (1)(cosx-sinx)/(cosx+sinx)+(cosx+sinx)/(cosx-s
求证 (1 + 2sinxcosx )/(sinx+cosx) = sinx + cosx
求证 sin^2x/(sinx-cosx)-(sinx+cosx)/tan^2 x-1=sinx+cosx
求证sinx * cosx(sinx+cosx)=(1+2sinx * cosx)/(secx+cscx)
证明:2(cosx-sinx)/1+sinx+cosx=cosx/1+sinx-sinx/1+cosx
求证[sinx(1+sinx)+cosx(1+cosx)][sinx(1-sinx)+cos(1-cosx)]=sin2
化简((sinx+cosx-1)(sinx-cosx+1)-2cosx)/sin2x
求证:sin2x/(1+sinx+cosx)=sinx+cosx-1
求证(1+sin2x)/(cosx+sinx)=cosx+sinx
1+sinx-cosx/1+sinx+cosx 化简