誘導(dǎo)公式作業(yè)5(一)-2024-2025學(xué)年高一上學(xué)期數(shù)學(xué)人教A版（2019）必修第一冊(cè)

作業(yè)49誘導(dǎo)公式(一)單選題每小題5分,共30分;多選題每小題6分,共18分1.化簡(jiǎn)sin2(π+α)-cos(π+α)·cos(-α)+1的結(jié)果為()A.1 B.2sin2α C.0 D.22.若sin(π+α)=12,α∈-π2,0,則tan(π-α)等于A.-12 B.-C.-3 D.33.已知tan(5π+x)=-2,則sinx-cosx2sinxA.4 B.3C.-3 D.-44.已知a=-13,b=-34,c=sin225°,則(A.c<a<b B.c<b<aC.a<c<b D.b<c<a5.(多選)已知sin(π-α)=13,則cos(α-2024π)的值為()A.223 B.-2236.(多選)已知△ABC的內(nèi)角A,B,C,下列式子中正確的有()A.sin(B+C)=sinAB.cos(B+C)=cosAC.tan(B+C)=tanAD.sin2A+cos2(B+C)=17.(5分)化簡(jiǎn):cos(3π-α)sin(π+α)8.(5分)已知sin(45°+α)=513,則sin(135°-α)=9.(10分)求值:tan150°cos(-210°)sin(-420°)sin1050°cos(-600°)10.(10分)化簡(jiǎn):(1)sin(540°+α)·(2)sin(2π+α)cos(-π+α)11.已知tanπ3-α=13,則tan2π3A.13 B.-C.23312.(多選)已知A=sin(kπ+α)sinα+cos(kπ+α)cosαA.-1 B.-2C.1 D.213.若cos5π6-θ=-23,θ∈0,π2,則sinA.23 B.-C.-53 D.14.(5分)化簡(jiǎn):1-2sin(π+6)cos(π+6)=.

15.(5分)已知α為第四象限角,化簡(jiǎn):1+sin(π-α)1+sin(π+α)16.(12分)已知f(α)=sin(π+α(1)化簡(jiǎn)f(α);(3分)(2)若α是第三象限角,且sin(α-π)=15,求f(α)的值;(4分(3)若α=-31π3,求f(α)的值.(5分

答案精析1.D2.D3.B4.D5.AB6.AD[依題意，在△ABC中，B+C=π-A，sin(B+C)=sin(π-A)=sinA，A正確；cos(B+C)=cos(π-A)=-cosA，B錯(cuò)誤；tan(B+C)=tan(π-A)=-tanA，C錯(cuò)誤；sin2A+cos2(B+C)=sin2A+cos2A=1，D正確.]7.-18.5解析sin(135°-α)=sin[180°-(45°+α)]=sin(45°+α)=5139.解原式=-tan150°cos210°sin420°=-tan(180°-30°)cos(180°+30°)sin(360°+60°)=-tan30°cos30°sin60°=-33×310.解(1)sin(540°+=sin(180°+=-sinα·cosα(2)sin(2π+=sinα(-cosα11.B[因?yàn)閠an2π=tanπ-=-tanπ3且tanπ3-α所以tan2π3+α=-12.BD[當(dāng)k為偶數(shù)時(shí)，A=sinαsinα+當(dāng)k為奇數(shù)時(shí)，A=-sinαsinα+-cos13.D[因?yàn)棣取?，所以5π6-θ∈π又因?yàn)閏os5π6-θ所以sin5π6-θ所以sinθ+π=sin5π6-θ=14.cos6-sin6解析原式=1-2sin6cos6=(cos6-sin6=|cos6-sin6|.因?yàn)?π2<6<2π所以cos6>0，sin6<0，因此cos6-sin6>0，所以原式=cos6-sin6.15.2解析依題意知α為第四象限角，所以1+sin(π-α)=1+sinα1-sin=(1+sinα(1-sinα=|1+sinα=1+sinα+1-sinα16.解(1)f(α)=-sinαcosα(2)∵sin(α-π)=-sin