Which expression completes the identity cos u sin v = ? a. 1/2[sin(u+v)+sin(u-v)] b. 1/2[cos(u-v)+cos(u+v)] c. 1/2[sin(u+v)-sin(u-v)] d. 1/2{cos(u-v)-cos(u+v)]

The product of trigonometric functions can be converted into sum ans vice versa. The given function is a product and we can convert it to a sum.One way is to expand the given expression and simplify it to find the result.

The second and easier option is to just remember the formulas of product to sum conversion identities. The 4 formulas for this case are listed below in the image.

Since we have the product of cos and sin, the sum will involve two sine functions connected by addition.

So the correct answer is option A