Verified answer

Объяснение:

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

[tex]\frac{sin(120\pi t)+sin(80\pi t)}{cos(120\pi t)-cos(80\pi t)}= \frac{2sin(100\pi t)*cos(20\pi t)}{-2sin(100\pi t)sin(20\pi t)} =-\frac{cos(20\pi t)}{sin(20\pi t)}=- ctg(20\pi t).[/tex]