Answer:
[tex]sin(6x) - sin(x)= 2cos(\frac{7x}{2}) * sin(\frac{5x}{2})[/tex]
Step-by-step explanation:
To write sin6x-sinx as a product , we use formula
[tex]sin(a) - sin(b)= 2cos(\frac{a+b}{2}) * sin(\frac{a-b}{2})[/tex]
We have 6x in the place of 'a' and x in the place of b
Replace it in the formula
[tex]sin(a) - sin(b)= 2cos(\frac{a+b}{2}) * sin(\frac{a-b}{2})[/tex]
[tex]sin(6x) - sin(x)= 2cos(\frac{6x+x}{2}) * sin(\frac{6x-x}{2})[/tex]
[tex]sin(6x) - sin(x)= 2cos(\frac{7x}{2}) * sin(\frac{5x}{2})[/tex]
