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

The general solution for tan(2θ)+tan(θ)=0 is θ=pin,θ=(2pi)/3+pin,θ= pi/3+pin

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tan(2θ)+tan(θ)=0

tan (2 θ) + tan (θ) = 0

θ = πn, θ = \frac{2 π}{3} + πn, θ = \frac{π}{3} + πn

Solution steps

tan (2 θ) + tan (θ) = 0

Rewrite using trig identities

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

Solve by substitution

tan (θ) = 0, tan (θ) = - 3, tan (θ) = 3

tan (θ) = 0 : θ = πn

tan (θ) = - 3 : θ = \frac{2 π}{3} + πn

tan (θ) = 3 : θ = \frac{π}{3} + πn

Combine all the solutions

θ = πn, θ = \frac{2 π}{3} + πn, θ = \frac{π}{3} + πn

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

4 cos (x) = 23

tan (x) = \frac{50}{50}

4 tan (θ) = 4

4 cos^{2} (x) - 8 cos (x) + 4 = 0

What is the general solution for tan(2θ)+tan(θ)=0 ?
The general solution for tan(2θ)+tan(θ)=0 is θ=pin,θ=(2pi)/3+pin,θ= pi/3+pin