Answer:
sin 4x - sin 6x = -2 cos 5x . sin x
Step-by-step explanation
We use the following result to solve this expression,
[tex]sin\,A-sin\,B=2\,cos\,(\frac{A+B}{2})\,sin\,(\frac{A-B}{2})[/tex]
and sin(-x) = -sin x
Consider,
sin 4x - sin 6x
[tex]=2\,cos\,(\frac{4x+6x}{2})\,sin\,(\frac{4x-6x}{2})[/tex]
[tex]=2\,cos\,(\frac{10x}{2})\,sin\,(\frac{-2x}{2})[/tex]
[tex]=2\,cos\,5x\,sin\,(-x)[/tex]
[tex]=2\,cos\,5x\,(-sin\,x)[/tex]
[tex]=-2\,cos\,5x\,sin\,x[/tex]
Therefore, sin 4x - sin 6x = -2 cos 5x . sin x
