Question

Write the product as a sum.
17 sin (x/2)cos(x/4)

Answer 1

`(17)/(2)\sin{(3x)/(4)}+(17)/(2)\sin{(x)/(4)}`

Explanation:

The appropriate identity is ...

`sin(\alpha)cos(\beta)=(1)/(2)(sin((\alpha+\beta))+sin((\alpha-\beta)))`

Filling in α=x/2 and β=x/4, we get ...

`17sin((x/2))cos((x/4))=(17)/(2)(sin((x/2+x/4))+sin((x/2-x/4)))\\\\=(17)/(2)\sin{(3x)/(4)}+(17)/(2)\sin{(x)/(4)}`