What is the expression?

Question

Answer 1

First of all, I would suggest that you download a "trigonometry identities cheat sheet" that has the trig identities. These are great helps for this type of problem.

The first hint in how to solve this is the fact that there is a sine and cosine together in the expression. This tells me that we are looking for the sine of a sum or difference of angles (or a combination).

For this problem, we will set a = 66^o and b = 86^o. Your equation is then: 2 sina cosb

The sine functions for the sum or difference of two angles are:

sin(a+b) = sina cosb + cosa sinb

sin(a-b) = sina cosb - cosa sinb

Notice the first term in both of these expressions has the sina cosb that is needed. You can then add these equations:

sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb = 2 sina cosb , which is your equation. Substitute the values of a and b into the expression