If α and β are acute angles satisfying cos 2α = (3 cos 2β - 1)/(3 - cos 2β)

Question

If α and β are acute angles satisfying cos 2α = \(\frac{\text{3 cos 2β - 1}}{\text{3-cos 2β}},\) then tan α =

A. \(\sqrt{2}\) tan β

B. \(\frac{1}{\sqrt{2}}\) tan β

C. \(\sqrt{2}\) cot β

D. \(\frac{1}{\sqrt{2}}\) cot β

Answer 1

Correct answer is A.

Then tan α is given by

Consider

applying square root on both sides