The formula for the product of the sine inverse of two variables, sin-1(x) and sin-1(y), is given by:
sin-1(x) * sin-1(y) = sin-1(x * y) + (1/2) * (sin-1(x) + sin-1(y))
This formula can be derived using the properties of sine and trigonometric identities. It helps simplify calculations involving the sine inverse function, particularly when dealing with the multiplication of two inverse sine values. When applying this formula, ensure that x and y fall within the appropriate range, typically between -1 and 1, for the inverse sine function to be defined.