Please Help ASAP!

1. Let $A$ be an angle such that $\tan(A)=\dfrac{1}{2}$. Find the value of $\tan(A+120^{\circ})$, giving your answer in simplest radical form.

2. $\cos \left(\frac\pi6 - \theta\right)$ can be expressed in the form $A\sin \theta + B\cos\theta$ where $A$ and $B$ are constants. What is the value of $\frac BA$?

3. Consider angles $x$ and $y$ such that $0 \le y \le x \le \frac\pi2$ and $\sin(x+y) = 0.9$ while $\sin(x-y) = 0.6$. What is the value of $(\sin x + \cos x)(\sin y + \cos y)$?

4. Suppose $\sin a + \cos b = -0.2$ while $\sin b + \cos a = 1.6$. What is the value of $\sin(a+b)$?

Any help on these would be greatly appreciated! Thanks!