Verified answer

Объяснение:

[tex]\frac{cos\alpha +cos3\alpha +cos5\alpha }{sin\alpha +sin3\alpha +sin5\alpha } =\frac{(cos\alpha +cos5\alpha) +cos3\alpha }{(sin\alpha +sin5\alpha) +sin3\alpha } =\frac{2*cos\frac{\alpha +5\alpha }{2}*cos\frac{\alpha -5\alpha }{2} +cos3\alpha }{2*sin\frac{\alpha +5\alpha }{2}*cos\frac{\alpha -5\alpha }{2} +sin3\alpha } =\\[/tex]

[tex]=\frac{2*cos3\alpha*cos(-2\alpha )+cos3\alpha }{2*sin3\alpha *cos(-2\alpha )+sin3\alpha } =\frac{cos3\alpha *(2*cos2\alpha +1)}{sin3\alpha *(2*cos2\alpha +1)}=\frac{cos3\alpha }{sin3\alpha } =ctg3\alpha .[/tex]