To verify the identity, we need to analyze and simplify both sides of the equation.
Let’s start with the left-hand side (LHS):
LHS = sin(x) * sin(y)
Now, let’s look at the right-hand side (RHS):
RHS = sin(x) * y + 2 * cos(x) * sin(y)
We need to manipulate the left-hand side to see if we can obtain the right-hand side. One way to approach this is to recall the product-to-sum identities. However, the given equation has a unique format, so we’ll try to reorganize terms directly instead.
Another approach could involve substituting values or applying trigonometric identities. However, in this specific case, we find that there may have been a misunderstanding in the identity’s format as they do not equate under common conditions.
If we analyze the structure, the term ‘y’ in the RHS does not have a corresponding term in the LHS, suggesting that the identity cannot be verified as written. Thus, we conclude that:
It seems that the presented identity has an error. Please double-check the identity for correctness.