Verified answer

Объяснение:

[tex]\boxed {cos\alpha +cos\beta =2cos\frac{\alpha +\beta }{2}cos\frac{\alpha -\beta }{2} }\\ \boxed {sin\alpha +sin\beta =2sin\frac{\alpha +\beta }{2}cos\frac{\alpha -\beta }{2} }[/tex]

[tex]\frac{cos12x+cos8x+cos4x}{sin12x+sin8x+sin4x}=\frac{(cos12x+cos4x)+cos8x}{(sin12x+sin4x)+sin8x}= \frac{2cos8xcos4x+cos8x}{2sin8xcos4x+sin8x}=\\ =\frac{cos8x*(2cos4x+1)}{sin8x*(2cos4x+1)}=\frac{cos8x}{sin8x} =ctg8x.[/tex]