+116 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!
