If ∝ + ß = \(\frac{π}{2}\) and ∝ : ß = 2 : 1 then ratio of tan∝ to tanß is?

3 : 1

∝ + ß = \(\frac{π}{2}\)

⇒ 2\(x\) + \(x\) = \(\frac{π}{2}\) ⇒ 3\(x\) = \(\frac{π}{2}\)

\(x\) = \(\frac{π}{6}\)

tan∝ = tan\(\frac{π}{3}\) = \(\sqrt {3}\),

tanß = tan\(\frac{π}{6}\) = \(\frac{1}{\sqrt {3 }}\)

tan∝ : tanß = \(\sqrt {3 }\) : \(\frac{1}{\sqrt {3 }}\) = 3 : 1