solve finding all solutions in 0 2 pi 3sec x x 2 tan2xSolut

solve, finding all solutions in (0, 2 pi). 3sec x x + 2 tan^2x

solve, finding all solutions in (0, 2 pi). 3sec x x + 2 tan^2x =0

given 3sec x + 2tan^2 x =0

sec^2 x -tan^2 x =1

sec^2 x -1 = tan^2 x

3sec x + 2(sec^2 x -1) =0

2sec^2 x +3sec x -2 =0

2sec^2 x +4sec x -sec x -2 =0

2secx(secx +2) -1(secx+2) =0

(secx +2) (2secx -1) =0

so secx = -2 or secx = 1/2

sec x = -2 or for this no solution

x = 2pi/3 , 4pi/3