Solve the equation for 0≤ Θ< 2pi

Question

2 tan Θ = 1+ tan² Θ

Answer 1

RHS equals sec²θ  LHS equals 2 sinθ / cosθ

 

2 sinθ / cosθ = 1 / cos²θ

 

multiply both sides by cos θ:  1/cosθ = 2sinθ

1 = 2 sinθcosθ

1 = sin(2θ)

 

I let you finish the problem.  Remember to give answers for all θ in interval (0, 2pi)