Question

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

Answer 1

Answer:

  $\dfrac{17}{2}\sin{\dfrac{3x}{4}}+\dfrac{17}{2}\sin{\dfrac{x}{4}}$

Step-by-step explanation:

The appropriate identity is ...

  $\sin{\alpha}\cos{\beta}=\dfrac{1}{2}(\sin{(\alpha+\beta)}+\sin{(\alpha-\beta)})$

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

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