Question

ребзи срочно
(cos 3beta + cos 5beta + cos beta)/(sin beta + sin 5beta + sin 3beta) = ctg * 3beta

Answer 1

Объяснение:

$\displaystyle\\\frac{cos3\beta +cos5\beta +cos\beta}{sin\beta +sin5\beta +sin3\beta } =\frac{cos3\beta +(cos5\beta +cos\beta) }{sin3\beta +(sin5\beta +sin5\beta) } =\frac{cos3\beta +2*cos\frac{5\beta +\beta }{2}*cos\frac{5\beta -\beta }{2} }{sin3\beta +2*sin\frac{5\beta +\beta }{2}*cos\frac{5\beta -\beta }{2} } =$

$\displaystyle\\=\frac{cos3\beta +2*cos3\beta *cos2\beta }{sin3\beta +2*sin3\beta *cos2\beta } =\frac{cos3\beta *(1+2cos2\beta )}{sin3\beta *(1+2cos2\beta )}=\frac{cos3\beta }{sin3\beta } =ctg3\beta .$