Avem formula
[tex]\sin{a}+\sin{b}=2\sin{\frac{a+b}{2}}\cos{\frac{a-b}{2}}[/tex]
Daca luam in considerare ultimul si primul termen al sumei
[tex]\sin{5x}+\sin{x}=2\sin{\frac{5x+x}{2}}\cos{\frac{5x-x}{2}}=2\sin{3x}\cos{2x}[/tex]
Inlocuim aceasta suma in suma initiala
[tex]\sin{3x}+2\sin{3x}\cos{2x}=(1+2\cos{2x})\sin{3x}[/tex]
