In ΔABC, ∠B = 90° and AB : BC = 2 : 1, then value of (sinA + cotC) = ?

A. $$3 + \sqrt 5 $$

B. $$\frac{{2 + \sqrt 5 }}{{2\sqrt 5 }}$$

C. $$2 + \sqrt 5 $$

D. $$3\sqrt 5 $$

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {\text{AC}} = \sqrt {{2^2} + {1^2}} = \sqrt 5 \cr & {\text{sin A}} + \operatorname{cotC} \cr & \frac{{{\text{BC}}}}{{{\text{AC}}}} + \frac{{{\text{BC}}}}{{{\text{AB}}}} \cr & \frac{1}{{\sqrt 5 }} + \frac{1}{2} \cr & \Rightarrow \frac{{2 + \sqrt 5 }}{{2\sqrt 5 }} \cr} $$