PQ.PQPQPQPQPQ32x,f(x)=ax+bx+cx+d=00f′′(x0)=0bbbx0=−2(−,f(−))3a3a3anmn2f(x)=(log,)(m≠0,n≠0)ax+ma2m2f(x+a)+f(x+b)=cca≠bT=2|b−a|2f(x+a)if(x+b)=cca≠bT=2|b−a|f(x)f(a+x)=f(b−x)1a+bf(x)x=21f(x)f(a+x)+f(b−x)=ca+bcf(x)⎛,⎞⎝⎜22⎠⎟)f(x)x=axbf(x)T2baf(x)a0b0f(x)T2baf(x)x=ab0f(x)T4ba)≥(cos(α−β)−cos(α+β)sinα⋅sinβ=2cos(α−β)+cos(α+β)cosα⋅cosβ=2sin(α+β)+sin(α−β)sinα⋅cosβ=2sin(α+β)−sin(α−β)cosα⋅sinβ=2、)sin)cosα+βα−β、、、sinα+sinβ=2sincos22α+βα−βsinα−sinβ=2cossin、(、、22α+βα−βcosα+cosβ=2coscos22αα++ββαα−−ββcosα−cosβ=−22sisninsisnin(2222θθθ2tan1−tan22tansinθ=2cosθ=2tanθ=2θθθ1+tan21+tan21−tan2222a)2(oα=(α−β)+β=(α+β)−βα+βα−ββ+αβ−αα=+=−22222α=(α+β)+(α−β)α=(α−β)+β=(α+β)−βα+ββα=(α−)−(−β)222α+βα−ββ+αβ−αα=+=−α−ββα2222=(α+)−(−β)2222α=(α+β)+(α−β)α−β=(α−γ)+(γ−β)α+ββα=(α−)−(−β)πππ222+α=−(−α)424α−ββα=(α+)−(−β)222α−β=(α−γ)+(γ−β)πππ+α=−(−α)424πABC∠ABC=2AC2=AB⋅ADBC2=AB⋅BDCD2=AD⋅BD111=+CD2AC2BC2ABCa,b,c6∠A,∠B,∠C222≥5abcosCccosB=+b=ccosA+acosCc=acosB+bcosAABCa,b,c6∠A∠B∠C2ABCsinA+sinB+sinC=4coscoscos222ABCcosA+cosB+cosC=1+4sinsinsin222sin2A+sin2B+sin2C=2+2cosAcosBcosCcos2A+cos2B+cos2C=1−2cosAcosBcosCsin2A−sin2B=sin(A−B)sin(A+B)tanA+tanB+tanC=tanA⋅tanB⋅tanC;2o2.o∞x2oABCDBC2AB2+AC2=2BD2+2AD21AD2=(2AB2+2AC2−BC2)4∞2∞21ABCAD∠BACABBD=ACDCSabc22S.)r=a+b+cabcabc.)R====4S2sinA2sinB2sinC).R.rR≥2rTTABCa,b,c6∠A∠B∠C2a2+b2+c2≥2abcosC+2accosB+2bccosAsinA>sinB⇔cos2A>cos2BsinA+sinB+sinC>cosA+cosB+cosC111tanA+tanB+tanC>++tanAtanBtanC2o2oAC2+BD2=AB2+BC2+CD2+DA2=2AB2+2BC2111)S=aha=ahb=ahc222111)2S=absinC=acsinB=bcsinA222a2sinBsinCb2sinAsinCc2sinAsinB)S===2sin(B+C)2sin(A+C)2sin(A+B)11)*(S=p(p−a)(p−b)(p−c)p=(a+b+c)=C222abc)*S=R.4Rabc)aS=2R2sinAsinBsinCS=4R1)*S=r(a+b+c)r.2,)*S=Rr(sinA+sinB+sinC)r.R.ABC)*S=4Rr(coscoscos)r.R.2221)2S=(c2sin2B+b2sin2C)41)S=(c22sinBcosB+b22sinCcosC)41)2S=(a2+b2−c2)tanC(C≠90°)4A1)S=p(p−a)tanp=(a+b+c)2221!!!2!!!2!!!!!!)S=ABAC−(ABiAC)221!!!!!!)*4S=x2y1−x1y2AB=(x,y)AC=(x,y)211221)*S=(x−x)(y−y)−(x−x)(y−y)A(x,y),B(x,y),C(x,y)2213131211122334x1y1111)**S=xy1A(x,y),B(x,y),C(x,y)p=(a+b+c)2221122332x3y314!!!!!!a2+b2−c2ABCABC26abcCB⋅CA=2