Алгебраические формулы

=В±Ö1-sin²a=(1-tg²a/2)/(1+tg²a/2)

sina=В±Ö1/1+ctg²a=(2tga/2)/(1+tg²a/2)

cos(a)=sinasinbcosacosb

sin(aВ±)=sinacosbВ±sinbcosa

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

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

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

ctg(a-)=(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=В±Ö1+cosa/2

sina/2=В±Ö1-cosa/2

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

ctga/2=В±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+cos=2cos(a+b)/2cos(a-b)/2

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

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

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

tgaВ±tg=(sin(aВ±b))/cosacosb

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

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

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

tga=(2tga/2)/(1-tg²a/2)

cosa=В±Ö1-sin²a=(1-tg²a/2)/(1+tg²a/2)

sina=В±Ö1/1+ctg²a=(2tga/2)/(1+tg²a/2)

cos(a)=sinasinbcosacosb

sin(aВ±)=sinacosbВ±sinbcosa

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

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

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

ctg(a-)=(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=В±Ö1+cosa/2

sina/2=В±Ö1-cosa/2

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

ctga/2=В±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+cos=2cos(a+b)/2cos(a-b)/2

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

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

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

tgaВ±tg=(sin(aВ±b))/cosacosb

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

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

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

tga=(2tga/2)/(1-tg²a/2)