What is the general solution for 4tan(x)-tan^2(x)=1 ?

The general solution for 4tan(x)-tan^2(x)=1 is x=0.26179…+pin,x=1.30899…+pin

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4tan(x)-tan^2(x)=1

4 tan (x) - tan^{2} (x) = 1

x = 0.26179 \dots + πn, x = 1.30899 \dots + πn

Solution steps

4 tan (x) - tan^{2} (x) = 1

Solve by substitution

tan (x) = 2 - 3, tan (x) = 2 + 3

tan (x) = 2 - 3 : x = arctan (2 - 3) + πn

tan (x) = 2 + 3 : x = arctan (2 + 3) + πn

Combine all the solutions

x = arctan (2 - 3) + πn, x = arctan (2 + 3) + πn

Show solutions in decimal form

x = 0.26179 \dots + πn, x = 1.30899 \dots + πn

x, arcsin (y) = arcsin (x) + \frac{( π )}{4}

18 sin^{2} (x) - 9 sin (x) = 0

3 sin^{2} (θ) + 6 sin (θ) - 11 = 7 sin (θ) - 9

x, 2 cos (x) - 3 = 0

tan (θ) = \frac{1.5}{9.81}

What is the general solution for 4tan(x)-tan^2(x)=1 ?
The general solution for 4tan(x)-tan^2(x)=1 is x=0.26179…+pin,x=1.30899…+pin