If sinθ + cosθ = √5sin(90 - θ), find the value of cotθ

A. $$\frac{{\sqrt 5 - 1}}{5}$$

B. $$\frac{{\sqrt 5 + 1}}{4}$$

C. $$\frac{{\sqrt 5 + 1}}{3}$$

D. $$\frac{{\sqrt 5 - 1}}{4}$$

Answer: Option B

Solution(By Examveda Team)

sinθ + cosθ = √5cosθ
sinθ = cosθ(√5 - 1)
$$\cot \theta = \frac{1}{{\sqrt 5 - 1}} \times \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}} = \frac{{\sqrt 5 + 1}}{4}$$