solve trigonometric equation

Question

solve the equation (tan t) (tan 2t)=1 for t ,t element [0,2pi)

Answer 1

Given that (tan t) (tan 2t) = 1

             => tan (t) * 2tan (t) / (1- tan^2(t) ) = 1  [ Since tan(2t) = 2tan (t) / (1- tan^2(t) ]

             => 2tan^2 (t) = 1 - tan^2(t)

             => 3 tan^2(t) = 1

             => tan^2(t) = 1/3

             => tan (t) = √(1/3)

             => tan (t) = +/- 1/√3

             => t = π/6, 5π/6, 7π/6, 11π/6

Therefore the values of t are π/6, 5π/6, 7π/6 and 11π/6.