Help With Parts III & IV - Stuck on Double Angle Formula

[nokia8650]

http://img103.imageshack.us/img103/637/trigrb3.th.jpg

I was having trouble with parts iii and iv. I have done i and ii. Please can someone help me with iii and iv. I do not really know where to start for iii and hence iv. I was thinking about the double angle formula for tan, but didnt know what to do with it.

Thanks

 

[Defennder]

For part 3, you are given
$$\tan x \tan y = -\frac{1}{2}$$

What do you get when you solve by the quadratic formulae for t?. Let one value be tan x, the other be tan y. Do they satisfy the above?

For part 4, solve by simultaneous equations A and B. Clearly you'll need to express $\tan (x+y)$ in terms of just tan x and tan y.

 

[chaoseverlasting]

There's an easier way to do this. Do you know how to find the product of roots for a quadratic? For a quadratic of the form $$ax^2+bx+c=0$$, the sum of the roots is $$\frac{-b}{a}$$ and the product is $$\frac{c}{a}$$.

Just look at the roots of the quadratic and the product of tanx tany...