sin(x+四分之派)=十分之七倍根号2,cos2x=25分之7,求cosx,只有一个答案,
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解决时间 2021-03-01 13:44
- 提问者网友:容嬷嬷拿针来
- 2021-02-28 16:13
sin(x+四分之派)=十分之七倍根号2,cos2x=25分之7,求cosx,只有一个答案,
最佳答案
- 五星知识达人网友:夜余生
- 2021-02-28 16:59
sin(x+π/4)=十分之七倍根号2>0,有2kπ<=x+π/4<=π+2kπ,即-π/4+2kπ<=x<=3π/4+2kπ
cos2x=7/25>0,有-π/2+2kπ<=2x<=π/2+2kπ,即-π/4+2kπ<=x<=π/4+2kπ
so,-π/4+2kπ<=x<=π/4+2kπ,有cosx>0
cos(2x)=(cosx)^2-(sinx)^2=(cosx-sinx)(cosx+sinx)=7/25
sin(x+π/4)=sinxcos(π/4)+cosxsin(π/4)=1/(根号2)*(sinx+cosx)=7/10*(根号2)
即sinx+cosx=7/5
有cosx-sinx=1/5
故cosx=4/5,符合题意
cos2x=7/25>0,有-π/2+2kπ<=2x<=π/2+2kπ,即-π/4+2kπ<=x<=π/4+2kπ
so,-π/4+2kπ<=x<=π/4+2kπ,有cosx>0
cos(2x)=(cosx)^2-(sinx)^2=(cosx-sinx)(cosx+sinx)=7/25
sin(x+π/4)=sinxcos(π/4)+cosxsin(π/4)=1/(根号2)*(sinx+cosx)=7/10*(根号2)
即sinx+cosx=7/5
有cosx-sinx=1/5
故cosx=4/5,符合题意
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