作业帮高数三道大题求解析17.化简sin(2π-α)cos(π/2+α)cos(π/2-α)/[sin(3π-α)sin(-π-α)sin(π/2+α)]=多少?18.若cos(α+π/3)=4/5,α∈（0,π/2）,则cosα=多少?19.已知函数f(x)=1+√2cos(2x-π/4)/[sin(x+π/2)](1)求f（x）的定义
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高数三道大题求解析17.化简sin(2π-α)cos(π/2+α)cos(π/2-α)/[sin(3π-α)sin(-π-α)sin(π/2+α)]=多少?18.若cos(α+π/3)=4/5,α∈（0,π/2）,则cosα=多少?19.已知函数f(x)=1+√2cos(2x-π/4)/[sin(x+π/2)](1)求f（x）的定义
高数三道大题求解析
17.化简sin(2π-α)cos(π/2+α)cos(π/2-α)/[sin(3π-α)sin(-π-α)sin(π/2+α)]=多少?
18.若cos(α+π/3)=4/5,α∈（0,π/2）,则cosα=多少?
19.已知函数f(x)=1+√2cos(2x-π/4)/[sin(x+π/2)]
(1)求f（x）的定义域；（2）若角α是第四象限角,且cosα=3/5,求f(α).
高数三道大题求解析17.化简sin(2π-α)cos(π/2+α)cos(π/2-α)/[sin(3π-α)sin(-π-α)sin(π/2+α)]=多少?18.若cos(α+π/3)=4/5,α∈（0,π/2）,则cosα=多少?19.已知函数f(x)=1+√2cos(2x-π/4)/[sin(x+π/2)](1)求f（x）的定义
17.化简sin(2π-α)cos(π/2+α)cos(π/2-α)/[sin(3π-α)sin(-π-α)sin(π/2+α)]=多少?
=（-sinα)(-sinα)sinα/[sinα(-sinα)cosα)=-tanα
18.若cos(α+π/3)=4/5,α∈（0,π/2）,则cosα=多少?
∵α∈（0,π/2）,∴α+π/3∈(π/3,5π/6)
∵cos(α+π/3)=4/5 ∴sin(α+π/3)=3/5
∴cosα=cos[(α+π/3)-π/3]
=cos(α+π/3)cosπ/3+sin(α+π/3)sinπ/3
=4/5*1/2+3/5*√3/2=(4+3√3)/10
19.已知函数f(x)=1+√2cos(2x-π/4)/[sin(x+π/2)]
(1)求f（x）的定义域；（2）若角α是第四象限角,且cosα=3/5,求f(α).
(1) sin(x+π/2)=cosx≠0,定义域{x|x≠kπ+π/2,k∈Z}
(2) f(x)=(1+cos2x+sin2x)/cosx
=(2cos²x+2sinxcosx)/cosx
=2(sinx+cosx)
∵角α是第四象限角,且cosα=3/5,
∴sinα=-4/5
∴f(α)= 2(sinα+cosα)=-2/5