Find all solutions in the interval [0, 2π). sec^2x-2= tan^2x no sol pi/3 pi/4 pi/6

8 sec^2 x + 4 tan^2 x − 12 = 0     →     sec^2x = tan^2x + 1

8 [ tan^2x + 1] + 4tan^2x - 12  = 0

8tan^2x + 8 + 4tan^2x - 12  = 0

12tan^2x - 4   = 0     divide through by 4

3tan^2x - 1  = 0

3tan^2x  =  1  

tan^2x  = 1/3      take the square root of both sides

tanx = ±1 / √3

And on the given interval, this happens at     pi/6 , 5pi/6, 7pi/6, 11pi/6

i hope this helps.

answer: 19 is   2

step-by-step explanation: i just looked at your answer and wrote it down