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

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

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1-2tan^2(θ)=-tan^2(θ)

1 - 2 tan^{2} (θ) = - tan^{2} (θ)

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

Solution steps

1 - 2 tan^{2} (θ) = - tan^{2} (θ)

Solve by substitution

tan (θ) = 1, tan (θ) = - 1

tan (θ) = 1 : θ = \frac{π}{4} + πn

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

Combine all the solutions

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

cos (a) = \frac{1}{3}

2 cos (2 θ) = 3

2 sin^{2} (θ) - 5 sin (θ) + 2 = 0

tan (2 x) + 1 = 0

sin (x) - 2 = - sin (x)

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