两角和与差的三角函数:
cos(+)=coscos-sinsin
cos(-)=coscos+sinsin
sin()=sincoscossin
tan(+)=(tan+tan)/(1-tantan)
tan(-)=(tan-tan)/(1+tantan)
三角和的三角函数:
sin(++)=sincoscos+cossincos+coscossin-sinsinsin
cos(++)=coscoscos-cossinsin-sincossin-sinsincos
tan(++)=(tan+tan+tan-tantantan)/(1-tantan-tantan-tantan)
辅助角公式:
Asin+Bcos=(A+B)^(1/2)sin(+t),其中
sint=B/(A+B)^(1/2)
cost=A/(A+B)^(1/2)
tant=B/A
Asin-Bcos=(A+B)^(1/2)cos(-t),tant=A/B
倍角公式:
sin(2)=2sincos=2/(tan+cot)
cos(2)=cos()-sin()=2cos()-1=1-2sin()
tan(2)=2tan/[1-tan()]
三倍角公式:
sin(3)=3sin-4sin()=4sinsin(60+)sin(60-)
cos(3)=4cos()-3cos=4coscos(60+)cos(60-)
tan(3)=tan a tan(/3+a) tan(/3-a)
半角公式:
sin(/2)=((1-cos)/2)
cos(/2)=((1+cos)/2)
tan(/2)=((1-cos)/(1+cos))=sin/(1+cos)=(1-cos)/sin
降幂公式:
sin()=(1-cos(2))/2=versin(2)/2
cos()=(1+cos(2))/2=covers(2)/2
tan()=(1-cos(2))/(1+cos(2))
万能公式:
sin=2tan(/2)/[1+tan(/2)]
cos=[1-tan(/2)]/[1+tan(/2)]
tan=2tan(/2)/[1-tan(/2)]
积化和差公式:
sincos=(1/2)[sin(+)+sin(-)]
cossin=(1/2)[sin(+)-sin(-)]
coscos=(1/2)[cos(+)+cos(-)]
sinsin=-(1/2)[cos(+)-cos(-)]
和差化积公式:
sin+sin=2sin[(+)/2]cos[(-)/2]
sin-sin=2cos[(+)/2]sin[(-)/2]
cos+cos=2cos[(+)/2]cos[(-)/2]
cos-cos=-2sin[(+)/2]sin[(-)/2]
推导公式:
tan+cot=2/sin2
tan-cot=-2cot2
1+cos2=2cos
1-cos2=2sin
1+sin=(sin/2+cos/2)
其他:
sin+sin(+2/n)+sin(+2*2/n)+sin(+2*3/n)++sin[+2*(n-1)/n]=0
cos+cos(+2/n)+cos(+2*2/n)+cos(+2*3/n)++cos[+2*(n-1)/n]=0 以及
sin()+sin(-2/3)+sin(+2/3)=3/2
tanAtanBtan(A+B)+tanA+tanB-tan(A+B)=0
cosx+cos2x+...+cosnx= [sin(n+1)x+sinnx-sinx]/2sinx