Given for α < 90° and β < 90° ,

Then tan α is given by

Consider

[using componendo and dividend principle, if ]

[ using cos 2x = 1- 2sin² x = 2cos²x – 1 ]

[ using cos 2x = cos² x – sin² x ]

[ using cos² x + sin² x = 1]

tan² α = 2 tan² β

applying square root on both sides

Hence the answer is option A.