If $$r\sin \theta = 1,$$   $$r\cos \theta = \sqrt 3 ,$$   then the value of $$\left( {\sqrt 3 {\text{tan}}\theta + 1} \right)$$   = ?

$$\eqalign{ & r\sin \theta = 1 \cr & r\cos \theta = \sqrt 3 \cr & \Rightarrow \frac{{{\text{ }}rsin\theta }}{{{\text{ }}r\cos \theta }} = \frac{1}{{\sqrt 3 }} \cr & \Rightarrow {\text{tan}}\theta = \frac{1}{{\sqrt 3 }} \cr & \Rightarrow \sqrt 3 {\text{tan}}\theta = 1 \cr & \left( {{\text{Add 1 both sides}}} \right) \cr & \Rightarrow \sqrt 3 {\text{tan}}\theta + 1 = 1 + 1 \cr & \Rightarrow \sqrt 3 {\text{tan}}\theta + 1 = 2 \cr} $$