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

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 6 sec^2 x + 3 tan^2 x       Log On


   

Question 1078820: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
6 sec^2 x + 3 tan^2 x - 9 = 0
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

6+sec%5E2%28x%29+%2B+3+tan%5E2%28x%29+-+9+=+0

6%281%2Btan%5E2%28x%29%5E%22%22%29%2B3tan%5E2%28x%29-9=0

6%2B6tan%5E2%28x%29%2B3tan%5E2%28x%29-9=0

9tan%5E2%28x%29-3=0

9tan%5E2%28x%29=3

tan%5E2%28x%29=1%2F3

tan%28x%29=%22%22+%2B-+sqrt%281%2F3%29

tan%28x%29=%22%22+%2B-+sqrt%283%29%2F3

You finish by yourself, using your knowledge of the special angles.

Edwin