20 баллов! 1. cos(a+b)cos(a-b)+sin(a+b)*sin(a-b) 2. tg(a+b)-tgb/1+tg(a+b)tgb 3....

Решите задачу:

$\mathtt{cos(a+b)cos(a-b)+sin(a+b)sin(a-b)=}\\\mathtt{cos[(a+b)-(a-b)]=cos[a+b-a+b]=cos2b}$

$\mathtt{\frac{tg(a+b)-tgb}{1+tg(a+b)tgb}=tg[a+b-b]=tga}$

$\mathtt{cos(a-\frac{\pi}{6})-\frac{1}{2}sina=cosacos(\frac{\pi}{6})+sinasin(\frac{\pi}{6})-\frac{1}{2}sina=}\\\mathtt{cosa*\frac{\sqrt{3}}{2}+sina*\frac{1}{2}-\frac{1}{2}sina=\frac{\sqrt{3}}{2}cosa}$