Which of the following is a solution to tan^2 x-1=0? a. 45 degrees, b. 120 degrees, c. 240 degrees, d. 330 degrees

Do you want a general solution or from 0 < = x < 2pi?

tan^2 (2x) - 1 = 0

tan^2 (2x) = 1

Take the square root of both sides,

tan (2x) = + / - 1

Two equations:

tan (2x) = 1

tan (2x) = - 1

Solve each equation.

tan (2x) = 1, 2x = {pi/4, 5pi/4, 9pi/4, 13pi/4},

x = { pi/8, 5pi/8, 9pi/8, 13pi/8 }

tan (2x) = - 1, 2x = { 3pi/4, 7pi/4, 11pi/4, 15pi/4 },

x = { 3pi/8, 7pi/8, 11pi/8, 15pi/8}

So for solutions within [0, 2pi),

x = {pi/8, 3pi/8, 5pi/8, 7pi/8, 9pi/8, 11pi/8, 13pi/8, 15pi/8 }