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

The general solution for tan^2(x)-tan(x)=2 is x=1.10714…+pin,x=(3pi)/4+pin

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

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

x = 1.10714 \dots + πn, x = \frac{3 π}{4} + πn

Solution steps

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

Solve by substitution

tan (x) = 2, tan (x) = - 1

tan (x) = 2 : x = arctan (2) + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = arctan (2) + πn, x = \frac{3 π}{4} + πn

Show solutions in decimal form

x = 1.10714 \dots + πn, x = \frac{3 π}{4} + πn

2 sin^{2} (\frac{x}{2}) - cos (\frac{x}{2}) = 0

cos (\frac{π}{4} - x) = \frac{12}{13}

x, y = f cos (x)

3 cot (2 x) = - 1, 0 \leq x \leq π

5 sin^{2} (x) - cos (x) = 2

What is the general solution for tan^2(x)-tan(x)=2 ?
The general solution for tan^2(x)-tan(x)=2 is x=1.10714…+pin,x=(3pi)/4+pin