解不等式x/√(1+x^2)>(x^2-1)/(x^2+1) 解不等式x/√(1+x^2)>(x^解不等式x/√(1+x^2)>(x^2-1)/(x^2+1)解不等式x/√(1+x^2)>(x^2-1)/(x^2+1)吴强芾  2010-8-110分钟内有问必答 前往下载令x=tanA,A∈(-π/2,π/2)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 10:40:00

解不等式x/√(1+x^2)>(x^2-1)/(x^2+1) 解不等式x/√(1+x^2)>(x^
解不等式x/√(1+x^2)>(x^2-1)/(x^2+1)
解不等式x/√(1+x^2)>(x^2-1)/(x^2+1)
吴强芾  2010-8-1
10分钟内有问必答 前往下载
令x=tanA,A∈(-π/2,π/2)
则原不等式可化为2sin^2A-sinA-1<0怎么化来的

x/√(1+x^2)>(x^2-1)/(x^2+1)
tanA/√(1+tan^2A)>(tan^2A-1)(tan^2A+1)
tanA/√(1+sin^2A/cos^2A)>(sin^2A/cos^2A-1)/(sin^2A/cos^2A+1)
tanA/√((cos^2A+sin^2A)/cos^2A)>(sin^2A-cos^2A)/cos^2A)/(sin^2A+cos^2A)/cos^2A)
tanA/√(1/cos^2A)>(-cos2A)
sinA+cos2A>0
sinA+1-2sin^2A>0
2sin^2A-sinA-1