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

## Trig Equation

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# 2 Answers

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.

If you regard the equation as a quadratic for tan

^{2}x, since sec^{2}x=-1+tan^{2}x, it is clear that there are no real solutions. the discriminant for tan^{4}x-tan^{2}x+2 is -7. Perhaps you meant something different.# Comments

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.

## 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 -7Comment