If α + β = 90° and α : β = 2 : 1, then the ratio of cosα to cosβ is?

Answer: Option A

$$\begin{array}{rl}& \alpha +\beta =90^{\circ }\\ & \text{and }\alpha :\beta =2:1\\ & 2x+x=90^{\circ }\\ & x=30^{\circ }\\ & \alpha =60^{\circ }\\ & \beta =30^{\circ }\\ & \frac{\text{cos }\alpha }{\cos \beta }\\ & =\frac{\cos {60}^{\circ }}{\cos {30}^{\circ }}\\ & =\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}\\ & =\frac{1}{2}\times \frac{2}{\sqrt{3}}\\ & =\frac{1}{\sqrt{3}}\\ & =1:\sqrt{3}\end{array}$$