What is the general solution for 6tan^4(x)-tan^2(x)-2=0 ?

The general solution for 6tan^4(x)-tan^2(x)-2=0 is x=0.68471…+pin,x=-0.68471…+pin

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6tan^4(x)-tan^2(x)-2=0

6 tan^{4} (x) - tan^{2} (x) - 2 = 0

x = 0.68471 \dots + πn, x = - 0.68471 \dots + πn

Solution steps

6 tan^{4} (x) - tan^{2} (x) - 2 = 0

Solve by substitution

tan (x) = \frac{2}{3}, tan (x) = - \frac{2}{3}, tan (x) = i \frac{1}{2}, tan (x) = - i \frac{1}{2}

tan (x) = \frac{2}{3} : x = arctan (\frac{2}{3}) + πn

tan (x) = - \frac{2}{3} : x = arctan (- \frac{2}{3}) + πn

tan (x) = i \frac{1}{2} :

No Solution

tan (x) = - i \frac{1}{2} :

No Solution

Combine all the solutions

x = arctan (\frac{2}{3}) + πn, x = arctan (- \frac{2}{3}) + πn

Show solutions in decimal form

x = 0.68471 \dots + πn, x = - 0.68471 \dots + πn

t, x = sin (t)

2 sin^{2} (x) - 2 = 0

2 tan^{2} (x) = 13

2 tan^{2} (x) = 15

1 - cos (θ) = 1 + cos (θ)

What is the general solution for 6tan^4(x)-tan^2(x)-2=0 ?
The general solution for 6tan^4(x)-tan^2(x)-2=0 is x=0.68471…+pin,x=-0.68471…+pin