Question

Write sin6x-sinx as a product.

Answer 1

`sin(6x) - sin(x)= 2cos((7x)/(2)) * sin((5x)/(2))`

Explanation:

To write sin6x-sinx as a product , we use formula

`sin(a) - sin(b)= 2cos((a+b)/(2)) * sin((a-b)/(2))`

We have 6x in the place of 'a' and x in the place of b

Replace it in the formula

`sin(a) - sin(b)= 2cos((a+b)/(2)) * sin((a-b)/(2))`

`sin(6x) - sin(x)= 2cos((6x+x)/(2)) * sin((6x-x)/(2))`

`sin(6x) - sin(x)= 2cos((7x)/(2)) * sin((5x)/(2))`