Реферат: Алгебраические формулы

cos a =±Ö1-sin2 a=(1-tg2 a/2)/(1+tg2 a/2) sin a =±Ö1/1+ctg2 a=(2tga/2)/(1+tg2 a/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+tg2 a) cos2 a =cos2 a-sin2 a=(1-tg2 a)/(1+tg2 a)=2cos2 a-1=1-2sin2 a
tg2 a =2tga/(1-tg2 a) ctg2 a =(ctg2 a-1)/2ctga ctg2 a =(ctg2 a-1)/2ctga
cos2 a /2 =1+cosa/2 cos2 a =(1+cos2a)/2 sin2 a /2 =1-cosa/2 sin2 a =(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 tg a ± tg b =( 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-tg2 a/2)
cos a =±Ö1-sin2 a=(1-tg2 a/2)/(1+tg2 a/2) sin a =±Ö1/1+ctg2 a=(2tga/2)/(1+tg2 a/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+tg2 a) cos2 a =cos2 a-sin2 a=(1-tg2 a)/(1+tg2 a)=2cos2 a-1=1-2sin2 a
tg2 a =2tga/(1-tg2 a) ctg2 a =(ctg2 a-1)/2ctga ctg2 a =(ctg2 a-1)/2ctga
cos2 a /2 =1+cosa/2 cos2 a =(1+cos2a)/2 sin2 a /2 =1-cosa/2 sin2 a =(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 tg a ± tg b =( 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-tg2 a/2)
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