How do I solve this finding all solutions?

Question

sec^2B-2tan^2B=0
Substitute pythagoreon identity
combine like terms simplify
find square root of both sides

Answer 1

sec^2 B - 2tan^2 B = 0
<=> 1/cos^2 B - 2 sin^2B / cos^2 B = 0
<=> (1 - 2 sin^2 B) / cos^2 B = 0
<=> sin^2 B = 1/2
<=> sin B = ± 1/√2
<=> B = (2k+1)π/4, for k ∈ Z.