Алгебраические формулы

cosa=±Ö1-sin2a=(1-tg2a/2)/(1+tg2a/2)	sina=±Ö1/1+ctg2a=(2tga/2)/(1+tg2a/2)
cos(a b)=sinasinb cosacosb	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(a b)=sinasinb cosacosb	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)