←Vrati se na zadatke1. ZadatakAko su xxx, yyy, aaa, bbb realni brojevi za koje vrijedi tgx+tgy=tga,ctgx+ctgy=ctgb,x+y=π4,\operatorname{tg}x+\operatorname{tg}y=\operatorname{tg}a,\quad\operatorname{ctg}x+\operatorname{ctg}y=\operatorname{ctg}b,\quad x+y=\frac\pi4,tgx+tgy=tga,ctgx+ctgy=ctgb,x+y=4π, izračunaj ctga−tgb\operatorname{ctg}a-\operatorname{tg}bctga−tgb.Prikaži rješenjeRješenjectga−tgb=1tgx+tgy−1ctgx+ctgy=1tgx+tgy−tgxtgytgx+tgy=1−tgxtgytgx+tgy=1tg(x+y)=1tgπ4=1\begin{aligned} \operatorname{ctg}a-\operatorname{tg}b&=\frac1{\operatorname{tg}x+\operatorname{tg}y}-\frac1{\operatorname{ctg}x+\operatorname{ctg}y}=\frac1{\operatorname{tg}x+\operatorname{tg}y}-\frac{\operatorname{tg}x\operatorname{tg}y}{\operatorname{tg}x+\operatorname{tg}y}\\ &=\frac{1-\operatorname{tg}x\operatorname{tg}y}{\operatorname{tg}x+\operatorname{tg}y}=\frac1{\operatorname{tg}(x+y)}=\frac1{\operatorname{tg}\frac\pi4}=1 \end{aligned}ctga−tgb=tgx+tgy1−ctgx+ctgy1=tgx+tgy1−tgx+tgytgxtgy=tgx+tgy1−tgxtgy=tg(x+y)1=tg4π1=1Pomakni formulu lijevo ili desno.
