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

The general solution for tan^2(x)=-1+2tan(-x) is x=(3pi)/4+pin

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Rewrite using trig identities

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

Subtract

- 1 - 2 tan (x)

from both sides

tan^{2} (x) + 1 + 2 tan (x) = 0

Solve by substitution

tan (x) = - 1

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

Combine all the solutions

x = \frac{3 π}{4} + πn

tan (2 θ) - tan (θ) = 0

cos (t) = - \frac{1}{2}

cos (2 θ) + cos (θ) = 0

4 sin (x) = 2

tan (4 x) = 1

What is the general solution for tan^2(x)=-1+2tan(-x) ?
The general solution for tan^2(x)=-1+2tan(-x) is x=(3pi)/4+pin