Question

sin x + sin y + sin (x+y)=? in produs

Answer 1

Răspuns:

Explicație pas cu pas:

$sinx+siny=2*sin\frac{x+y}{2}*cos\frac{x-y}{2}\\sin(x+y)=sin(2*\frac{x+y}{2})=2*sin\frac{x+y}{2}*cos\frac{x+y}{2}.\\deci~sinx+siny+sin(x+y)=2*sin\frac{x+y}{2}*cos\frac{x-y}{2}+2*sin\frac{x+y}{2}*cos\frac{x+y}{2}=2*sin\frac{x+y}{2}*(cos\frac{x-y}{2}+cos\frac{x+y}{2}).$