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

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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）的定义域；（2）若角α是第四象限角,且cosα=3/5,求f(α).

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

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 (1+sinα+cosα)*[sin(α/2)-cos(α/2)]/√(2+2cosα)化简（3/2*π 已知(3sinα+cosα)/(3cosα-sinα)=2,则2-3sin（α-3π）sin（1.5π-α）-[cos（化简sin(α-5π)/cos(3π-α)×cos(π/2-α)/sin(α-3π)×cos(8π-α)/sin(-α- 比较大小sin(cosα)与cos(sinα)（0＜α＜π/2) α∈（0,π／2 ）,比较 sin(cosα) 与cos(sinα)大小已知tanα=2,sinα+cosα＜0,求[sin(2π-α)*sin(π+α)*cos(-π+α)]/[sin(3π 化简:sin(2π-α)cos(π/2+α)+sin(3π/2-α)cos(π-α)= 若（sinα+cosα）/（sinα-cosα）=2 则sin(α-5π)·sin(3π/2-α)=? 若sinα+cosαsinα−cosα=2，则sin（α-5π）•sin（3π2-α）等于（　　） α属于（0,π/2）且2sin²α-sinαcosα-3cos²α=0求sin(α+π/4)/sin 化简[sin(π/2-α）cos(π/2-α)]/cos(π+α)-[sin(π-α)cos(π/2-α)]/sin(π