Trig Equation

Question

sec^2 x - tan ^4 x = 3              Solve for x

Answer 1

If you regard the equation as a quadratic for tan²x, since sec²x=-1+tan²x, it is clear that there are no real solutions.  the discriminant for tan⁴x-tan²x+2 is -7. Perhaps you meant something different.

Answer 2

 Just need to convert the Trigonometric function to one function like tanX

  

     Sec²X - tan⁴ X =- 3

 

     Tan² X + 1 - Tan⁴ X = -3

 

      - Tan⁴ X + Tan² X + 1 + 3 = 0

     

         Tan⁴  X - Tan² X  - 4 = 0

 

        (  Tan²  X  - 4 ) ( Tan² X +1 ) =0  

 

         Tan ² X = 4        Tan² X +1 = 0  ( Has no acceptable answer.)

 

          Tan X = ± 2         X = 63.4 °        X = - 63.4°

                                     X = 243.7°       X =  153.4°

 

               These are answers between range of  0 < X < 360°

 

               For all possible answer add 2n( 360° ) to each 4 X values.

      

          Note that 3 was changed to -3, for plus 3 there is no real solution.