學(xué)必求其心得，業(yè)必貴于專精松滋一中單元測(cè)試題29（數(shù)學(xué)4必修)第三章三角恒等變換［綜合訓(xùn)練B組]一、選擇題1．設(shè)a1cos63sin6,b2tan13,c1cos50,則有（）221tan2132A.abcB.abcC.acbD。bca22．函數(shù)y1tan22x的最小正周期是（）1tan2xA．B．C．D．2423．sin163sin223sin253sin313（)．3A．1．1C．3D2B2224．已知sin(x)3,則sin2x的值為（）45A。19B.16C.14D.7252525255．若A．

(0,),且cossin1，則cos2(）317B．1799C．17D．17936．函數(shù)A．

ysin4xcos2x的最小正周期為(）B．C．D．242二、填空題1．已知在ABC中,3sinA4cosB6,4sinB3cosA1,則角C的大小為．sin65o＋sin15osin10o2．計(jì)算：sin25o－cos15ocos80o的值為_______．學(xué)必求其心得，業(yè)必貴于專精3．函數(shù)ysin2xcos(2x)的圖象中相鄰兩對(duì)稱軸的距離是．3364．函數(shù)5．已知

f(x)cosx1cos2x(xR)的最大值等于．2f(x)Asin(x)在同一個(gè)周期內(nèi)，當(dāng)xπ時(shí)，f(x)獲取最大值為32，當(dāng)x0時(shí)，f(x)獲取最小值為2，則函數(shù)f(x)的一個(gè)表達(dá)式為______________．三、解答題1。求值:（1）sin60sin420sin660sin780;（2）sin2200cos2500sin200cos500。2．已知AB4，求證：(1tanA)(1tanB)23．求值：log2cos249log2cos9log2cos9.4．已知函數(shù)f(x)a(cos2xsinxcosx)b(1）當(dāng)a0時(shí),求f(x)的單調(diào)遞加區(qū)間;學(xué)必求其心得，業(yè)必貴于專精(2)當(dāng)a0且x[0,]時(shí)，f(x)的值域是[3,4],求a,b的值。2答案一、選擇題1.C2.B3.B

asin300cos6cos300sin6sin240,bsin260,csin250,1tan22x2ytan22xcos4x,T214sin17(sin43)(sin73)(sin47)cos17cos43sin17sin43cos6004.D5.A

sin2xcos(2x)cos2(4x)12sin2(x)72425(cossin)21,sincos4，而sin0,cos099cossin(cossin)24sincos173cos2cos2sin2(cossin)(cossin)1(17)336。By(sin2x)2cos2x(sin2x)2sin2x1(sin2x1)23241cos22x31(1cos4x)34484二、填空題1。6(3sinA4cosB)2(4sinB3cosA)237,2524sin(AB)37sin(AB)1,sinC1，事實(shí)上A為鈍角，C2262。23sin(800150)sin150sin100sin800cos150cos15023sin(150100)cos150cos800sin150cos100sin150學(xué)必求其心得，業(yè)必貴于專精3.3ysin2xcos2xcos6sin2xsincos2xcossin2xsin6233363632x),T23,相鄰兩對(duì)稱軸的距離是周期的一半cos(23634.3f(x)cos2xcosx1,當(dāng)cosx1時(shí),f(x)max342245．f(x)2sin(3x)A2,T,T22,3,sin1,可取22332三、解答題1。解:(1）原式

sin60cos120cos240cos480sin60cos60cos120cos240cos480cos601sin120cos120cos240cos4801sin240cos240cos4802cos604cos601sin480cos4801sin9601cos60181616cos60cos60cos6016（2）原式1cos4001cos10001(sin700sin300)22211(cos1000cos400)1sin70012243sin700sin3001sin70034242。證明:AB,tan(AB)tanAtanB1,1tanAtanB4得tanAtanB1tanAtanB,1tanAtanBtanAtanB2(1tanA)(1tanB)23.解：原式log2(coscos2cos4),99924sincoscos2cos41而coscos99999cos989sin9學(xué)必求其心得，業(yè)必貴于專精即原式log21384.解：f(x)a1cos2xa1sin2xb2asi