10-2

10-2 was super easy because there were only two formulas to remember and you only need tan for them. I was going to do 10-3 but I did that last week lol.

The formulas are:
tan(a+b) = tan(a)+tan(b)/1-tan(a)tan(b)

tan(a-b) = tan(a)-tan(b)/1+tan(a)tan(b)

The sign on top is the same as in what you are doing, and the bottom sign is opposite of the top.

Ex. 1

Suppose tan(a) = 1/2 and tan(b) = 3/4. Find tan(a+b) and tan (a-b)

tan(a+b) = tan(a)+tan(b)/1-tan(a)tan(b)

Replacing, you get (1/2)+(3/4)/1-(1/2)(3/4)

Simplifying, it becomes (10/8)/1-(3/8) = (10/8)/(5/8) = 80/40 = 2

tan(a-b) = tan(a)-tan(b)/1+tan(a)tan(b)

Replacing, you get (1/2)-(3/4)/1+(1/2)(3/4)

Simplifying, it becomes (-2/8)/1+(3/8) = (-2/8)/(11/8) = -16/88 = -2/11