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# Trig Equation

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

### 2 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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

TanX - Tan2 X  - 4 = 0

(  Tan 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.

- Tan4 X + Tan2 X + 1 - 3 = 0 copied from your solution becomes
-tan4x+tan2x-2=0 or tan4x-tan2x+2=0 whose discriminant is -7
Thank  you , so I changed it to -3, where there is  a solution . We keep both of them. It doesn't seem like the intention of the problem was for no solution. But we keep both of them on. It is a good exercise.
Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
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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.