What is the general solution for tan(2θ)-tan(θ)=0 ?

The general solution for tan(2θ)-tan(θ)=0 is θ=pin

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tan(2θ)-tan(θ)=0

tan (2 θ) - tan (θ) = 0

θ = πn

Solution steps

tan (2 θ) - tan (θ) = 0

Rewrite using trig identities

\frac{tan ( θ ) + tan ^{3} ( θ )}{1 - tan ^{2} ( θ )} = 0

Solve by substitution

tan (θ) = 0, tan (θ) = i, tan (θ) = - i

tan (θ) = 0 : θ = πn

tan (θ) = i :

No Solution

tan (θ) = - i :

No Solution

Combine all the solutions

θ = πn

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

cos (2 θ) + cos (θ) = 0

4 sin (x) = 2

tan (4 x) = 1

cos (3 x) + cos (x) = 0

What is the general solution for tan(2θ)-tan(θ)=0 ?
The general solution for tan(2θ)-tan(θ)=0 is θ=pin