Solution
Given : α + β = 90° and α:β = 2:1
Let $$\alpha=2x$$ and $$\beta=x$$
=> $$2x+x=90^\circ$$
=> $$x=\frac{90}{2}=30^\circ$$
=> $$\alpha = 60^\circ$$ and $$\beta=30^\circ$$
$$\therefore$$ $$\frac{cos\alpha}{cos\beta}=\frac{cos(60^\circ)}{cos(30^\circ)}$$
= $$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}$$
=> Ans - (A)
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