^{2}X - tan

^{4}X =- 3

^{2}X + 1 - Tan

^{4}X = -3

^{4}X + Tan

^{2}X + 1 + 3 = 0

^{4 }X - Tan

^{2}X - 4 = 0

^{2 }X - 4 ) ( Tan

^{2}X +1 ) =0

^{2}X = 4 Tan

^{2}X +1 = 0 ( Has no acceptable answer.)

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

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

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

Sec^{2}X - tan^{4} X =- 3

Tan^{2} X + 1 - Tan^{4} X = -3

- Tan^{4} X + Tan^{2} X + 1 + 3 = 0

Tan^{4 }X - Tan^{2} X - 4 = 0

( Tan^{2 } X - 4 ) ( Tan^{2} X +1 ) =0

Tan ^{2} X = 4 Tan^{2} 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.

But:

Sin^{2} X + Cos^{2}X = 1

Sin^{2} X / Cos^{2 }X + 1 = Sec^{2} X

1 + Tan^{2 }X = sec^{2} X

So , substitution in 2nd line is correct.

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## Comments

^{4}X + Tan^{2}X + 1 - 3 = 0 copied from your solution becomes^{4}x+tan^{2}x-2=0 or tan^{4}x-tan^{2}x+2=0 whose discriminant is -7