Question

Докажите тождество .............

Answer 1

$\frac{Sin3\alpha+Sin\alpha}{Cos\alpha+Cos3\alpha}*Cos^{2}2\alpha=\frac{2Sin\frac{3\alpha+\alpha}{2}*Cos\frac{3\alpha-\alpha}{2}}{2Cos\frac{\alpha+3\alpha}{2}*Cos\frac{\alpha-3\alpha}{2}} *Cos^{2}2\alpha=\frac{Sin2\alpha}{Cos2\alpha}*Cos^{2}2\alpha=\\=Sin2\alpha Cos2\alpha=0,5*2Sin2\alpha Cos2\alpha=0,5Sin4\alpha$