We are asked to fill in the blank to complete the following trigonometric formula.
sin (u-v) =
Let's start by recalling all the sum and difference formulas.
Sum and Difference Formulas
sin (u+v) = sin u cos v + cos u sin v
sin (u-v) = sin u cos v -cos u sin v
cos (u+v) = cos u cos v - sin u sin v
cos (u-v) = cos u cos v +sin u sin v
tan (u+v) = tan u + tan v/1 - tan u tan v
tan (u-v) = tan u - tan v/1 + tan u tan v
Next, let's look for the formula that contains the expression sin (u-v).
Sum and Difference Formulas
sin (u+v) = sin u cos v + cos u sin v
sin (u-v) = sin u cos v -cos u sin v
cos (u+v) = cos u cos v - sin u sin v
cos (u-v) = cos u cos v +sin u sin v
tan (u+v) = tan u + tan v/1 - tan u tan v
tan (u-v) = tan u - tan v/1 + tan u tan v
According to one of the formulas from the table, sin (u-v) is equal to sin u cos v -cos u sin v. With this in mind, let's complete the given formula.
sin (u-v) = sin u cos v -cos u sin v
