Question

cos3a+cos5a+cos7a+cos9a помогите умру

Answer 1

$(cos3a+cos5a)+(cos7a+cos9a)=\\=2cdot cos frac{3a+5a}{2} cdot cosfrac{5a-3a}{2} +2cdot cos frac{7a+9a}{2} cdot cosfrac{9a-7a}{2}=\\=2cdot cos4acdot cosa+2cdot cos8acdot cosa= \\=2cosacdot (cos4a+cos8a)=2cosacdot 2cdot cos6acdot cos2a=\\=4cdot cosacdot cos2acdot cos6a$