Răspuns:
a)[tex]\frac{sin(x+30)+sin(x+60)}{cos(x+30)+cos(x+60)}=[/tex]
Voi face separat sin(x+30)+sin(x+60) si cos(x+30)+cos(x+60) pentru a se intelege mai bine
[tex]sin(x+30)+sin(x+60)=2sin\frac{x+30+x+60}{2}*cos\frac{x+30-x-60}{2}=\\=2sin\frac{2x+90}{2}*cos \frac{-30}{2} = 2sin(x+45)*cos(15)[/tex]
[tex]cos(x+30)+cos(x+60)=2cos\frac{x+30+x+60}{2}*cos\frac{x+30-x-60}{2} =\\=2cos\frac{2x+90}{2}*cos\frac{-30}{2} = 2cos(x+45)*cos(15)[/tex]
Inlocuim in ecuatie:
[tex]\frac{2sin(x+45)*cos(15)}{2cos(x+45)*cos(15)} =\frac{sin(x+45)}{cos(x+45)} = tg(x+45)[/tex]
