Формулы по тригонометрии шпаргалка

cosa=±Ö1-sin2a=(1-tg2a/2)/(1+tg2a/2)	sin a=±Ö1/1+ctg2a=(2tga/2)/(1+tg2a/2)
cos( a b )=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)
sin2 a=2sinacosa=(2tga)/(1+tg2a)	cos2 a=cos2a-sin2a=(1-tg2a)/(1+tg2a)=2cos2a-1=1-2sin2a
tg2 a=2tga/(1-tg2a) ctg2a=(ctg2a-1)/2ctga	ctg2 a=(ctg2a-1)/2ctga
cos2 a /2=1+cosa/2   cos2a=(1+cos2a)/2	sin2 a /2=1-cosa/2                    sin2a=(1-cos2a)/2
cos a /2=±Ö1+cosa/2	sin a /2=±Ö1-cosa/2
tg a /2=±Ö1-cosa/1+cosa=(sina)/(1+cosa)=(1-cosa)/sina	ctg a /2=±Ö1+cosa/1-cosa=sina/(1-cosa)=(1+cosa)/sina
sin a +cos a=Ö2 cos(P/4-a)	sin a -cos a=Ö2 sin(a-P/4)
cos a -sin a=Ö2 sin(P/4-a)	cos a +cos b=2cos(a+b)/2cos(a-b)/2
cos a -cos b=-2sin(a+b)/2sin(a-b)/2	sin a +sin b=2sin(a+b)/2cos(a-b)/2
sin a -sin b=2sin(a-b)/2cos(a+b)/2	tga ±tgb =(sin(a±b))/cosacosb
cos a cos b =1/2(cos(a-b)+cos(a+b))	sin a sin b=1/2(cos(a-b)-cos(a+b))
sin a cos b=1/2(sin(a+b)+sin(a-b))	tg a=(2tga/2)/(1-tg2a/2)

cosa=±Ö1-sin2a=(1-tg2a/2)/(1+tg2a/2)	sin a=±Ö1/1+ctg2a=(2tga/2)/(1+tg2a/2)
cos( a b )=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)
sin2 a=2sinacosa=(2tga)/(1+tg2a)	cos2 a=cos2a-sin2a=(1-tg2a)/(1+tg2a)=2cos2a-1=1-2sin2a
tg2 a=2tga/(1-tg2a)             ctg2a=(ctg2a-1)/2ctga	ctg2 a=(ctg2a-1)/2ctga
cos2 a /2=1+cosa/2               cos2a=(1+cos2a)/2	sin2 a /2=1-cosa/2                                sin2a=(1-cos2a)/2
cos a /2=±Ö1+cosa/2	sin a /2=±Ö1-cosa/2
tg a /2=±Ö1-cosa/1+cosa=(sina)/(1+cosa)=(1-cosa)/sina	ctg a /2=±Ö1+cosa/1-cosa=sina/(1-cosa)=(1+cosa)/sina
sin a +cos a=Ö2 cos(P/4-a)	sin a -cos a=Ö2 sin(a-P/4)
cos a -sin a=Ö2 sin(P/4-a)	cos a +cos b=2cos(a+b)/2cos(a-b)/2
cos a -cos b=-2sin(a+b)/2sin(a-b)/2	sin a +sin b=2sin(a+b)/2cos(a-b)/2
sin a -sin b=2sin(a-b)/2cos(a+b)/2	tga ±tgb =(sin(a±b))/cosacosb
cos a cos b =1/2(cos(a-b)+cos(a+b))	sin a sin b=1/2(cos(a-b)-cos(a+b))
sin a cos b=1/2(sin(a+b)+sin(a-b))	tg a=(2tga/2)/(1-tg2a/2)