Question

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.

cos(a-п/6)-0,5sina

Answer 1

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

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

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