Question Detail
Question
If \(\alpha + \beta = 90^\circ\) and \(\alpha : \beta = 2:1\), then what is the ratio of \(\cos \alpha\) to \(\cos \beta\)?
Correct Answer
Option C is the correct answer.
Detailed Explanation
α:β = 2:1 and α+β=90° ⇒ 2k + k = 90 ⇒ 3k=90 ⇒ k=30, so β=30°, α=60°. cos60° = 1/2, cos30° = √3/2, so cosα : cosβ = (1/2) : (√3/2) = 1 : √3.
Hint
Find the actual angles first using the ratio and sum.