This Is An Example Of A Sum and Difference Problem

To begin, find two solvable angles that add up to 105 degrees.

Then plug in the two angles that add up to the first angle you had and put them in a formula so both angles are cosine and that product is subtracted by the product of the sin of the two angles. Now convert the angles to points. 

Multiply
Subtract the fractions, you already have a common denominator and you cannot simplify any further so here is your answer. 

This Is An Example of A Double Angle Problem

Here is the basic formula for all double angle problems. What you are going to do in a double angle problem is similar to what you did in the sum and difference problem.

This Is An Example Of A Half Angle Problem

Now this type of problem is generally used to solve for an angle less than thirty or something that is easier to divide than add up to. Now I hope you all can figure out that thirty divided by two does equal fifteen. Also figure out the point at cosine thirty. Not copy, change, flip.  Now you cannot simplify any further so here is your answer.