To prove the given equation, we can use the sum-to-product identities for sine and cosine:
Adding these two equations together, we get:
sin(s + t) + sin(s - t) = sin(s)cos(t) + cos(s)sin(t) + sin(s)cos(t) - cos(s)sin(t)= 2sin(s)cos(t)
Therefore, the equation sin(s + t) + sin(s - t) = 2sin(s)cos(t) is proven.
To prove the given equation, we can use the sum-to-product identities for sine and cosine:
sin(s + t) = sin(s)cos(t) + cos(s)sin(t)sin(s - t) = sin(s)cos(t) - cos(s)sin(t)Adding these two equations together, we get:
sin(s + t) + sin(s - t) = sin(s)cos(t) + cos(s)sin(t) + sin(s)cos(t) - cos(s)sin(t)
= 2sin(s)cos(t)
Therefore, the equation sin(s + t) + sin(s - t) = 2sin(s)cos(t) is proven.