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

The general solution for tan^2(2θ)=tan(2θ) is θ= pi/8+(pin)/2 ,θ=(pin)/2

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tan^2(2θ)=tan(2θ)

tan^{2} (2 θ) = tan (2 θ)

θ = \frac{π}{8} + \frac{πn}{2}, θ = \frac{πn}{2}

Solution steps

tan^{2} (2 θ) = tan (2 θ)

Solve by substitution

tan (2 θ) = 1, tan (2 θ) = 0

tan (2 θ) = 1 : θ = \frac{π}{8} + \frac{πn}{2}

tan (2 θ) = 0 : θ = \frac{πn}{2}

Combine all the solutions

θ = \frac{π}{8} + \frac{πn}{2}, θ = \frac{πn}{2}

2 cos (2 x) = 2 sin (x)

- sin (θ) + 1 + cos (θ) = 0

sin (x) = \frac{1}{10}

θ, sin (θ) = 0

sec (2 z - \frac{π}{6}) = 2

What is the general solution for tan^2(2θ)=tan(2θ) ?
The general solution for tan^2(2θ)=tan(2θ) is θ= pi/8+(pin)/2 ,θ=(pin)/2