If r = 1, r = 3 , then the value of ( 3 tan + 1 ) = ?

Answer: Option D

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