Need some help with trigonometry related questions

[Baalzamon]

For problem #2, you have to use this identity: Tan{X( /-)Y]= [Tan[X]( /-)Tan[Y]} / {1(-/ )Tan[X]Tan[Y]}

The /- indicates whether or not you are adding or subtracting.  The next /- is written in the same way, so you will use the same symbol, however, the final one is written as -/ , which indicates you will do the opposite of what you did for the first two.

So you have: Tan (120-45)= [Tan (120) - Tan (45)] / [1 Tan (120) Tan (45)]

You can simplify this to the following: [-sqrt(3) - 1] / [1 - sqrt(3)]

In order to simplify that, you have to multiply both the top and the bottom by: [1 sqrt(3)], which is simply the bottom function with its sign changed.

When you do this, you will get: [-2sqrt(3) - 4] / (-2)

All values are negatives, so you can get rid of the minus signs.  You then need to divide both the top values by 2 so you won't have a denominator, which results in: sqrt(3) 2

Hope that helps :D