Use the product to sum formula to fill in the blanks in the identity below: sin(7x)cos(4x)=1/2(sin(_____x)+sin(______x))

Question

please provide all steps for the solution

Answer 1

The product identity states that:

sin(a)cos(b) = 0.5[sin(a+b) + sin(a-b)]

Using this identity, we can plug in "a" and "b":

sin(7x)cos(4x) = 0.5[sin(7x + 4x) + sin(7x - 4x)]

= 0.5[sin(11x) + sin(3x)]