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- #1

^{2}2x - 1 = 0. Find all solutions from 0 to 2pi

1.) sqrt(tan

^{2}2x) = sqrt(1)

2.) tan2x = +- 1 (reason for two quadratic equations in #4)

3.) use double angle identity for tan and rationalize to form two quadratic equations:

4.) tan

^{2}x + 2tanx - 1 AND tan

^{2}x -2tanx -1

5.) now I use quadratic equation but I've come to a roadblock with the second equation in #4 because I'm getting irrational solutions: (1 +- sqrt(2))

6.) I'm trying to find exact answer in radians. I'm not even sure I'm getting a correct answer. I'm totally stumped here and need help before moving on.