常用三角函数公式

三角函数公式两角和公式sin(A+B)=sinAcosB+cosAsinBsin(A-B)=sinAcosB-cosAsinBcos(A+B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=tanAtanB-1tanB+tanAtan(A-B)=tanAtanB1tanBtanAcot(A+B)=cotAcotB1-cotAcotBcot(A-B)=cotAcotB1cotAcotB倍角公式tan2A=Atan12tanA2sin2A=2sinA•cosAcos2A=cos2A-sin2A=2cos2A-1=1-2sin2A三倍角公式sin3A=3sinA-4(sinA)3cos3A=4(cosA)3-3cosAtan3A=tanA·tan(3+A)·tan(3-A)半角公式sin2A=2cos1Acos2A=2cos1Atan2A=AAcos1cos1cot2A=AAcos1cos1tan2A=AAsincos1=AAcos1sin和差化积sina+sinb=2sin2bacos2basina-sinb=2cos2basin2bacosa+cosb=2cos2bacos2bacosa-cosb=-2sin2basin2batana+tanb=babacoscos)sin(积化和差sinAsinB=-21[cos(A+B)-cos(A-B)]cosAcosB=21[cos(A+B)+cos(A-B)]sinAcosB=21[sin(A+B)+sin(A-B)]cosAsinB=21[sin(A+B)-sin(A-B)]万能公式sina=2)2(tan12tan2aacosa=22)2(tan1)2(tan1aatana=2)2(tan12tan2aa其它公式a•sina+b•cosa=)b(a22×sin(a+c)(其中tanc=ab)a•sina-b•cosa=)b(a22×cos(a-c)(其中tanc=ba)1+sina=(sin2a+cos2a)21-sina=(sin2a-cos2a)2其他非重点三角函数csca=asin1seca=acos1双曲函数sinha=2e-e-aacosha=2ee-aatgha=aacoshsinh平方关系22sincos1xx22secn1xtax22csccot1xx倒数关系tancot1xxseccos1xxcsin1csxx商数关系sintancosxxxcoscotsinxxx正弦定理RCcBbAa2=sin=sin=sin(R为三角形内切圆半径)余弦定理Cabbaccos2+=222Cabbakcos2222(k为三角形过点C中线长度的2倍)