Question

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

Answer 1

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 }