Verified answer

Объяснение:

[tex]\boxed {cos\alpha -cos\beta =2*sin\frac{\beta-\alpha }{2} *sin\frac{\beta+\alpha }{2}}\\ cos(x)-cos(3x)=2*sin\frac{3x-x}{2} *sin\frac{3x+x}{2} =2sin(\frac{2x}{2} )sin(\frac{4x}{2} )=2sin(x)sin(2x).[/tex]