Find all solutions of the equation in the interval 0 2 Enter

Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 6 sec2 x + 3 tan2 x 9 = 0

Solution

6 sec²x + 3 tan²x 9 = 0

we have identity  sec²x - tan²x =1 => sec²x = tan²x +1

6(tan²x +1) + 3 tan²x 9 = 0

6tan²x +6+ 3 tan²x 9 = 0

9tan²x 3 = 0

9tan²x = 3

tan²x = 3/9

tan²x = 1/3

tanx = -1/3,tanx = 1/3

x=5/6 ,11/6 , x=/6,7/6

x=/6 ,5/6,7/6,11/6 are the solutions