用向量推导正、余弦及正切的两角和差和二倍角与半角公式!

a=(cosu,sinu),b=(cosv,sinv)cos(u-v)=a∙b=(cosu,sinu)∙(cosv,sinv)=cosu cosv +sinu sinv------------------(1)2.a=(cosu,sinu),b=(cos(-v),sin(-v))=(cosv,-sinv)cos(u+v)=a∙b=(cosu,sinu)∙(cosv,-sinv)=cosu cosv -sinu sinv--------------------(2)3.a=(cosu,sinu),b=(cosv,sinv)sin(u-v)=(axb) (在一个平面上)=cosu sinv - cosv sinu-------------------------(3)4. a=(cosu,sinu),b=(cos(-v),sin(-v))=(cosv,-sinv)sin(u+v)=ax(-b)(在一个平面上)=cosu sinv +cosv sinu------------------(4)5.tan(u+v)=sin(u+v)/cos(u+v)=[tanu+tanv]/[1-tanu tanv] (从(2),(4))6. tan(u-v) (从(1),(3))7.设 u=v, 从(4),sin2u=2sinu cosu8. 设 u=v, 从(2), cos2u= (cosu)^2-(sinu)^2----------(5)9.设x=2u, 从(5), cosx=(cosx/2)^2-(sinx/2)^2-------------(6)cosx=1-2(sinx/2)^2,
sin(x/2)=[(1-cosx)/2]^(1/2)10. 从(6) cosx=(cosx/2)^2-1+(cosx/2)^2cos(x/2)=[(1+cosx)/2]^(1/2)