Question

How do you verify that the x values `pi/12, (5pi)/12` are solutions to `3tan^2 2x-1=0`?

Answer 1

Use Trig table of special arcs -->
#x = pi/12 --> 2x = pi/6 --> tan (pi/6) = sqrt3/3 --> tan^2 (pi/6) = 3/9 --> 3tan^2 2x - 1 = 9/9 - 1 = 0#. Proved!

`x = (5pi)/12 --> 2x = (5pi)/6 --> tan ((5pi)/6) = -sqrt3/3 -->tan^2 ((5pi)/6) = 3/9 --> 3 tan^2 (2x) - 1 = 9/9 - 1 = 0`. Proved