Question

Решить. ctg п/6 sin2a - tg п/3 cos^2 2a при a=п/24

Answer 1

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)