sin(a+b),cos(a+b)展开式

请问为什么 sin(a b)=sinacosb cosasinb,有没有详细推导呢?
sin(a b) sin(b-a)/cos(a b)-cos(b-a)=-cota 证明
a^2[sin(a-b)-sin(a b)]=b^2[-sin(a b)-sin(a-b)]怎么得
tana-tanb/tana tanb=sin(a-b)/sin(a b) 请问是怎么证明的,谢
化简:cos(a b)cosa sin(a b)sina