Trig Table and unit circle -->
tan (pi/4) = 1 and tan (pi/4 + pi) = tan ((5pi)/4) = 1
Substitute in the right side of the equation 1 by tan (pi/4), and 1 by tan ((5pi)/4):
a. tan (2x + pi/3) = 1 = tan (pi/4)
2x + pi/3 = pi/4 + kpi
2x = pi/4 - pi/3 = - pi/12 + kpi --> x1 = - pi/24 + (kpi)/2
x1 = - pi/24 = ((23pi)/24) + (kpi)/2 (co-terminal arc)
If k = 1 --> x2 = (23pi)/24 + pi/2 = (35pi)/24
b. tan (2x + pi/3) = tan ((5pi)/4)
2x + pi/3 = (5pi)/4 + kpi
2x = (5pi)/4 - pi/3 = (11pi)/12 + kpi --> x3 = (11pi)/24 + (kpi)/2
If k = 1 --> x4 = (11pi)/24 + pi/2 = (33pi)/24
Answers for (0, 2pi):
(11pi)/24 , (23pi)/24 , (33pi)/24, (35pi)/24
