If $$r\sin \theta = 1,$$ $$r\cos \theta = \sqrt 3 ,$$ then the value of $$\left( {\sqrt 3 {\text{tan}}\theta + 1} \right)$$ = ?
A. $$\sqrt 3 $$
B. $$\frac{1}{{\sqrt 3 }}$$
C. 1
D. 2
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & r\sin \theta = 1 \cr & r\cos \theta = \sqrt 3 \cr & \Rightarrow \frac{{{\text{ }}rsin\theta }}{{{\text{ }}r\cos \theta }} = \frac{1}{{\sqrt 3 }} \cr & \Rightarrow {\text{tan}}\theta = \frac{1}{{\sqrt 3 }} \cr & \Rightarrow \sqrt 3 {\text{tan}}\theta = 1 \cr & \left( {{\text{Add 1 both sides}}} \right) \cr & \Rightarrow \sqrt 3 {\text{tan}}\theta + 1 = 1 + 1 \cr & \Rightarrow \sqrt 3 {\text{tan}}\theta + 1 = 2 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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