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

The general solution for 2tan^2(θ)cos(θ)-tan^2(θ)=0 is θ=pin,θ= pi/3+2pin,θ=(5pi)/3+2pin

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2tan^2(θ)cos(θ)-tan^2(θ)=0

2 tan^{2} (θ) cos (θ) - tan^{2} (θ) = 0

θ = πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

2 tan^{2} (θ) cos (θ) - tan^{2} (θ) = 0

Factor

2 tan^{2} (θ) cos (θ) - tan^{2} (θ) : tan^{2} (θ) (2 cos (θ) - 1)

tan^{2} (θ) (2 cos (θ) - 1) = 0

Solving each part separately

tan^{2} (θ) = 0 or 2 cos (θ) - 1 = 0

tan^{2} (θ) = 0 : θ = πn

2 cos (θ) - 1 = 0 : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

1 + 2 cot (θ) - 2 cot^{2} (θ) = - 3 cot^{2} (θ)

3 arctan (2 x) = π

sin (x) - 9 = cos (x) - 9

7 sin (x) + 1 = 5 sin (x)

sec (x) + tan (x) = 1, (0, 2 π)

What is the general solution for 2tan^2(θ)cos(θ)-tan^2(θ)=0 ?
The general solution for 2tan^2(θ)cos(θ)-tan^2(θ)=0 is θ=pin,θ= pi/3+2pin,θ=(5pi)/3+2pin