Формулы по тригонометрии (шпаргалка)

cosa=±Ö1-sin²a=(1-tg²a/2)/(1+tg²a/2)

sina=±Ö1/1+ctg²a=(2tga/2)/(1+tg²a/2)

cos(ab)=sinasinbcosacosb

sin(a±b)=sinacosb±sinbcosa

tg(a+b)=sin(a+b)/cos(a+b)=(tga+tgb)/(1-tgatgb)

tg(a-b)=(tga-tgb)/(1+tgatgb)

ctg(a+b)=(ctgactgb-1)/(ctga+ctgb)

ctg(a-b)=(ctgactgb+1)/(ctgb-ctga)

sin2a=2sinacosa=(2tga)/(1+tg²a)

cos2a=cos²a-sin²a=(1-tg²a)/(1+tg²a)=2cos²a-1=1-2sin²a

tg2a=2tga/(1-tg²a)ctg2a=(ctg²a-1)/2ctga

ctg2a=(ctg²a-1)/2ctga

cos²a/2=1+cosa/2   cos²a=(1+cos2a)/2

sin²a/2=1-cosa/2                     sin²a=(1-cos2a)/2

cosa/2=±Ö1+cosa/2

sina/2=±Ö1-cosa/2

tga/2=±Ö1-cosa/1+cosa=(sina)/(1+cosa)=(1-cosa)/sina

ctga/2=±Ö1+cosa/1-cosa=sina/(1-cosa)=(1+cosa)/sina

sina+cosa=Ö2 cos(P/4-a)

sina-cosa=Ö2 sin(a-P/4)

cosa-sina=Ö2 sin(P/4-a)

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

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

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

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

tga±tgb=(sin(a±b))/cosacosb

cosacosb=1/2(cos(a-b)+cos(a+b))

sinasinb=1/2(cos(a-b)-cos(a+b))

sinacosb=1/2(sin(a+b)+sin(a-b))

tga=(2tga/2)/(1-tg²a/2)

cosa=±Ö1-sin²a=(1-tg²a/2)/(1+tg²a/2)

sina=±Ö1/1+ctg²a=(2tga/2)/(1+tg²a/2)

cos(ab)=sinasinbcosacosb

sin(a±b)=sinacosb±sinbcosa

tg(a+b)=sin(a+b)/cos(a+b)=(tga+tgb)/(1-tgatgb)

tg(a-b)=(tga-tgb)/(1+tgatgb)

ctg(a+b)=(ctgactgb-1)/(ctga+ctgb)

ctg(a-b)=(ctgactgb+1)/(ctgb-ctga)

sin2a=2sinacosa=(2tga)/(1+tg²a)

cos2a=cos²a-sin²a=(1-tg²a)/(1+tg²a)=2cos²a-1=1-2sin²a

tg2a=2tga/(1-tg²a)             ctg2a=(ctg²a-1)/2ctga

ctg2a=(ctg²a-1)/2ctga

cos²a/2=1+cosa/2               cos²a=(1+cos2a)/2

sin²a/2=1-cosa/2                                sin²a=(1-cos2a)/2

cosa/2=±Ö1+cosa/2

sina/2=±Ö1-cosa/2

tga/2=±Ö1-cosa/1+cosa=(sina)/(1+cosa)=(1-cosa)/sina

ctga/2=±Ö1+cosa/1-cosa=sina/(1-cosa)=(1+cosa)/sina

sina+cosa=Ö2 cos(P/4-a)

sina-cosa=Ö2 sin(a-P/4)

cosa-sina=Ö2 sin(P/4-a)

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

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

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

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

tga±tgb=(sin(a±b))/cosacosb

cosacosb=1/2(cos(a-b)+cos(a+b))

sinasinb=1/2(cos(a-b)-cos(a+b))

sinacosb=1/2(sin(a+b)+sin(a-b))

tga=(2tga/2)/(1-tg²a/2)