高中数学常用解题公式结论.pdf

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1、 学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571!#$!#$%&%&()*+,-.()*+,-./!#$%&%&$!#$%&%()*#$%&%()*!#$%#&!#$%#()+%&,-./01*%&,-./01*2 2*(+(,)-)3 3456789%:;%456789%:;%2 2?%&A()BC*%&A()BC*$!#$()()$D DE(FGH*E(FGH*)I I;)J)KBC*;)J)KBC*)L LM)NOBC*M)NOBC*)P PQRSQRSTUVW*TUVW*./0/1/(/231/(+.30313(32/13(),.4567&89:;%)-.4

2、&89:;%)X XYZSTUVW*YZSTUVW*.?1?(1()+.?1(1(?1?()!)T_*)T_*)!)#ab)#ab)!+!+)cab)cab)!3!3)deS*)deS*ABC()!?!?)MfS*)MfS*ADEF()!D!Dgh)M)i*gh)M)i*G&H()!I!Igh)J)i*gh)J)i*G&H()!L!Lgh)jki*gh)jki*G&H()2n12n-ABAAB=ABABA=ABABABAB=()()()()n ABn An Bn AB=+-!21.414,31.732,52.236,3.142,2.718epnmnmaa=log1log;logloglogca

3、acbbbbaa=()()()000()()yyfxxx-=-minmax()0()0f xf xmaxmin()0()0f xf x或()()f axf bx+=+Tba=-()()f axf bx+=-2abx+=()()()f xyf xf y=+()logaf xx=()()()f xyf x f y+=()xf xa=()()()f xyf xf y+=+()f xkx=学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571!P!Pgh)lmi*gh)lmi*G&H()!X!Xgh)n)i*gh)n)i*G&HIJ)+o(./pqC*o(./pqC*)+!+!rs

4、tWu*rstWu*KLMNOP)+vwxyz*vwxyz*)+3+3|*QR S%T7UVWXYZ)QR%TQR S YZ)$!*#$)+)+$+?+?q)BC*q)BC*)+D+Dq)BC*q)BC*)+I+Iqk)BC*qk)BC*2+L+Lqk)BC*qk)BC*2+P+Pq)TS*q)TS*G&H)+X+Xqk)TS*qk)TS*G&H)33q*q*G_$a&H)3!3!qk*qk*G_b$a&H)3+3+WW!*G&Hc)3333WW+*G&Hc)3?3?WW 3 3*G&Hc)()fxc=()f xcxb=+()()fxf x=()xf xke=()0f x=1ln(1)1(0)

5、ln1xxexxxexxx+-=-当且仅当时“”成立()()()()limlimxaxaf xfxg xg x=()0()0f xg x或maxmin(1)()()(2)()()af xaf xaf xaf x(1)()()()()0h xf xg xh x=-minmax()()f xg x1(1)naand=+-11()(1)22nnn aan nSnad+-=+11nnaa q-=11(1)11nnnaa qaqSqq+-=-mnpq+=+mnpqaaaa+=+mnpq+=+mnpqa aa a=,a A b2Aab=+,a G b2Gab=111(1)1n nnn-+=1111nnTn

6、n=-=+1111(2)22n nnn-+=1111(1)2212nTnn=+-+111111nnnnaadaa+=-111 11()nnTd aa+=-学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571 3D3DWW?*G&Hc)3I3IW8C*W8C*)$!,#$-.()-.()$)3L3L)T*)T*5d%(ed%(5f%(gh%)3P3PnBC*nBC*i63j:;&klmnopq(r63js;&kltuopqv)3X3XBC*BC*Twxxw&kl:yZ)+Txxww&klzyZ),T|zyZ)?BC*BC*“222222222222222222”222222

7、2222222222222?!?!KBC*KBC*“22”2?+?+BCBC 2?3?3j*j*2?*“2”221111(21)(21)2 2121nnnn-+-+=11(1)221nTn=-+11 12()1(1)1nn nndq bba b qabTqqq-=+-sinyra=cosxra=tanyxa=22rxy=+ppsin()sincoscossinababab=cos()coscossinsinababab=!tantantan()1tantanababab=!sin22sincosaaa=2222cos2cossin1 2sin2cos1aaaaa=-=-=-22tantan21

8、 tanaaa=-sin2sincos2aaa=21 cos2sin2aa-=21 cos2cos2aa+=22sincossin().(tan,0)bawxbwxabwxaajj+=+=2sinsinsinabcRABC=222222cos2cos2bcaAabcbcAbc+-=+-222222cos2cos2acbBbacacBac+-=+-222222cos2cos2abcCcababCab+-=+-学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571?D?DH*H*h#gDMIz_MB=&=($!/#$0101$?I?IWWTT*“&h”()?L?LWWTT*“z

9、|&()?P?PT*T*KSPYJ)KPY)?X?XT*T*KSPY)J)KPY)DDT)BC*T)BC*KSPY)J)KPY)D!D!TBC*TBC*KSPY)J)KPY)D+D+_-T-TQQ 2 2KSPY)J)KPY)D3D3|bbo_Wo_W*KSP#c#()KP)$!2 2#$34563456)D?D?WBC*WBC*2DDDD-*KSPY%(KPY%)DIDI-*KSPY%)(KPY%)DLDLb-b-*KSPY%(KPY%)ABBCAC+=!CCA-AB=B!/=abbal!1221/0abx yx y-=!0aba b=!1 2120abx xy y+=!cosa ba bq

10、=!1 212=a b x xy y+!cos=a ba bq!121222221122cos=x xy yxyxyq+a!aea=!1122221111=,xyaeaxyxy=+!,AB AC!(1)PAxPByPC xy=+=!cosa ba bq=!sina ma mq=!sinxhaq=cosm nm nq=!cosSSq=射影原图xm ABhm=!1 12xS hhS=学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571 DPDP-T*-T*2DXDX_T*_T*2IIT*T*2I!I!jT*jT*2I+I+jTS*jTS*%&%)I3I3j*j*fr%&r%&

11、)I?I?j-T*j-T*%&5%)IDIDj-*j-*fr&r&)$!7 7#$89568956)IIIITT G&HA-A)ILILTT GHA-FA)IPIPTT)GHA-FA)LLT*T*%Az_AA-)L!L!TTCC_*(F:F)L+L+TTCC_*(F:F)123nVrSSS=+2222Rabc=+222()22sinhRrarA=+=222()2sinRrhRarA=+-=32ha=234Sa=36ra=33Ra=21Rr=32ha=斜63ha=正rR31Rr=rRh+=正PAPBPAB12122(2)PFPFaaFF+=P1 2F F2a12122(2)PFPFaaFF-=P

12、1 2F F2a(,0)2pF2px=-Pbkxy+=y(0,)Bbxxmya=+x(,0)A ax 学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571 L3L3*I2L?L?*I2LDLDbbBC*bbBC*22222LILIbBC*bBC*2LLLL BC*BC*2LPLPbWbWTBCTBC*2LXLXBC*BC*2PPTTBCBC*22P!P!BCBC*2 2KSPh%(KP%KP%)P+P+BC*BC*2 2KSPh%(KP%(KP%)P3P3bBC*bBC*2 2KSPh%(KP%(KP%)PPTb*Tb*2P!P!Tb-*Tb-*22P+P+b-*b-*2

13、2P3P3T*T*rF2P?P?TBC*TBC*2PDPDTBC*TBC*2)(/212121bbkkll=01221=-BABA12121-=kkll02121=+BBAA212212)()(yyxxAB-+-=2200BACByAxd+=1222CCdAB-=+220022000,b xb xpkkka ya yy=-=双椭抛2212121()4lkxxx x=+-()4)11(212212yyyykl-+=222lrd=-0,MFaex=0,MFexa=20pxMF+=2(1cos)baea2(1cos)baea1 cospa2222(1cos)baea-2222(1cos)baea-2

14、2sinpa2122222sinkplxxppka+=+=122tan2F PFSbq=!122cot2F PFSbq=!b221cbeaa=-22211cbekaa=+=+渐 学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571 PIPITTBCBC*2PLPLBC*BC*2PPPPTBC*TBC*2PXPXb*b*dAzf(2XXbS*bS*2X!X!bTt*bTt*2X+X+ETyz*ETyz*2X3X3yz*yz*KSPJ)KPJ)KPTZ)X?X?Tyz*Tyz*AA%)KSP%J)KP%J)KP%J)XDXD;yz*;yz*)$!:#$;)XIXI_T_T2

15、2-*-*($)XLXL_T*_T*(|M)()XPXP_T)*_T)*Ahv)XXXX_T)*_T)*)!_T)*_T)*I6&_.M Av)!_T_*_T_*21cos1elal-=+22bPQa=2PQp=112,AFBFp+=22212121212222,4pkpx xxxpy ypyykk+=+=-+=2121yyxxOBOA+=1212(,)OAOBxx yy+=+!AOB0OA OB!AOBOAOB0OA OB=!PABPAPB0PA PB!12120kkkk=-+=iiiinfSydN=121nfff+=121nSSS+=123123nnxx fxfx fx f=+中中中中12

16、3123nnxx Sx Sx Sx S=+中中中中x22221212()()()nnsxxfxxfxxf=-+-+-中中中 学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571!+!+iBC*iBC*2 2!3!3EiBC*EiBC*2 2!?!?Tyz*Tyz*$z#=)!D!DBC*BC*2!I!IT&yz*T&yz*=)!L!L&BC*&BC*2!P!PHHBCBC*2!X!X_BCBC*2!BC*BC*2 2!MxBC*MxBC*2!+!+xBC*xBC*22!3!3x#l(BC*x#l(BC*2!?!?E;TBC*E;TBC*2!D!D;TBC*;TBC*2!I

17、!I;T;THH*(X%v)$!?#$ABCABC)!L!L_N*_N*22!P!P b bT_*T_*2!X!X b bT_*T_*2!+!+_T-obTBC*T-obTBC*2()AnP AnW=()AAAlSVP AlSVWWW=(1)(1)mnAn nnm=-+(1)(1)(1)3 2 1mnn nnmCm m-+=-nnpxpxpxXE+=2211)(2221122()()()()nnD XxE xpxE xpxE xp=-+-+-()()()P ABP AP B+=+()1()P AP A=-()()()P ABP A P B=()1()P ABP AB+=-()kn kMN Mn

18、NC CP xkC-=()(1)kkn knP xkC pp-=-()E Xnp=()(1)D Xnpp=-22,tancos,sinyxyxxyrqrqrq=+=a()Rqa r=aqa=(0)qa r=()Rqa r=2121212()4ABrrrrr r=-=+-学习资料分享/升学政策解读/优质师资推荐 咨询电话：18020133571!+!+!T!)_*T!)_*T$Z(2!+!+T!)_*T!)_*T$Z2!+3!+3T!)_*T!)_*$2!+?!+?!)!)TT!222222222!+D!+D!)!)TT+22!+I!+I!)!)TT 332 22!+L!+L!)!)TT?22cossinxarybrqq=+=+qcossinxatybtaa=+=+tcossinxaybqq=qt12,PAtPBt=t1 2PA PBtt=t212121 2()4ABtttttt=-=+-t1212121212ttttPAPBtttttt+=+=-、同号、异号