solve for x tan2x secx 1 0 for x E 0 2pi A 0 2pi3 4pi3 B 0

solve for x tan²x + secx -1 = 0 for x E [0, 2pi)

A) 0, 2pi/3, 4pi/3

B) 0, pi / 3 , 4pi / 3

C.) 2pi / 3 , 4pi / 3, 2pi

tan^2x + secx -1 = 0

use the identity: 1+tan^2x = sec^2x

So, sec^2x +secx -2 =0

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

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

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

secx =1 ----> cosx =1

x= 0, 2pi

secx =-2

cosx = -1/2

x = pi-pi/3 ,pi +pi/3 = 2pi/3 , 4pi/3

x = 2pi/3, 4pi/3

Solution : x= 0, 2pi/3, 4pi/3 , 2pi

Opition A and C