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sin(a+b)=sinacosb+cosasinb

sin(a-b)=sinacosb-sinbcosa §R

cos(a+b)=cosacosb-sinasinb

cos(a-b)=cosacosb+sinasinb

tan(a+b)=(tana+tanb)/(1-tanatanb)

tan(a-b)=(tana-tanb)/(1+tanatanb)

cot(a+b)=(cotacotb-1)/(cotb+cota) Ÿ

cot(a-b)=(cotacotb+1)/(cotb-cota)

±¶½Ç¹«Ê½

tan2a=2tana/[1-(tana)^2]

cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2

sin2a=2sina*cosa

°ë½Ç¹«Ê½

sin(a/2)=¡Ì((1-cosa)/2) sin(a/2)=-¡Ì((1-cosa)/2)

cos(a/2)=¡Ì((1+cosa)/2) cos(a/2)=-¡Ì((1+cosa)/2)

tan(a/2)=¡Ì((1-cosa)/((1+cosa)) tan(a/2)=-¡Ì((1-cosa)/((1+cosa))

cot(a/2)=¡Ì((1+cosa)/((1-cosa)) cot(a/2)=-¡Ì((1+cosa)/((1-cosa)) ¥Q

tan(a/2)=(1-cosa)/sina=sina/(1+cosa)

ºÍ²î»¯»ý

2sinacosb=sin(a+b)+sin(a-b)

2cosasinb=sin(a+b)-sin(a-b) )

2cosacosb=cos(a+b)-sin(a-b)

-2sinasinb=cos(a+b)-cos(a-b)

sina+sinb=2sin((a+b)/2)cos((a-b)/2

cosa+cosb=2cos((a+b)/2)sin((a-b)/2)

tana+tanb=sin(a+b)/cosacosb

»ý»¯ºÍ²î¹«Ê½

sin(a)sin(b)=-1/2*[cos(a+b)-cos(a-b)]

cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)]

sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)]

ÓÕµ¼¹«Ê½

sin(-a)=-sin(a)

cos(-a)=cos(a)

sin(pi/2-a)=cos(a)

cos(pi/2-a)=sin(a)

sin(pi/2+a)=cos(a)

cos(pi/2+a)=-sin(a)

sin(pi-a)=sin(a)

cos(pi-a)=-cos(a)

sin(pi+a)=-sin(a)

cos(pi+a)=-cos(a)

tga=tana=sina/cosa

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sin(a)= (2tan(a/2))/(1+tan^2(a/2))

cos(a)= (1-tan^2(a/2))/(1+tan^2(a/2))

tan(a)= (2tan(a/2))/(1-tan^2(a/2))

ÆäËü¹«Ê½

a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c) [ÆäÖУ¬tan(c)=b/a]

a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c) [ÆäÖУ¬tan(c)=a/b]

1+sin(a)=(sin(a/2)+cos(a/2))^2

1-sin(a)=(sin(a/2)-cos(a/2))^2

ÆäËû·ÇÖصãÈý½Çº¯Êý

csc(a)=1/sin(a)

sec(a)=1/cos(a)

Ë«Çúº¯Êý

sinh(a)=(e^a-e^(-a))/2

cosh(a)=(e^a+e^(-a))/2

tgh(a)=sinh(a)/cosh(a)