Алгебраические формулы

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)