Question

Cos3a+cos5a+cos7a+cos9a помогите умру

Answer 1

$(cos3a+cos5a)+(cos7a+cos9a)=\\\\=2\cdot cos \frac{3a+5a}{2} \cdot cos\frac{5a-3a}{2} +2\cdot cos \frac{7a+9a}{2} \cdot cos\frac{9a-7a}{2}=\\\\=2\cdot cos4a\cdot cosa+2\cdot cos8a\cdot cosa= \\\\=2cosa\cdot (cos4a+cos8a)=2cosa\cdot 2\cdot cos6a\cdot cos2a=\\\\=4\cdot cosa\cdot cos2a\cdot cos6a$