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

The general solution for 2tan^2(θ)sin(θ)-tan^2(θ)=0 is θ=pin,θ= pi/6+2pin,θ=(5pi)/6+2pin

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2tan^2(θ)sin(θ)-tan^2(θ)=0

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

θ = πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

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

Factor

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

tan^{2} (θ) (2 sin (θ) - 1) = 0

Solving each part separately

tan^{2} (θ) = 0 or 2 sin (θ) - 1 = 0

tan^{2} (θ) = 0 : θ = πn

2 sin (θ) - 1 = 0 : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin^{2} (x) = - 3 sin (x) + 4

tan^{2} (x) csc (x) = tan^{2} (x)

12.3 = 2.3 sin (24 x) + 14.1

7 sec^{2} (x) - 7 = 0

- 5 cos^{2} (θ) - 9 sin (θ) + 8 = - sin (θ)

What is the general solution for 2tan^2(θ)sin(θ)-tan^2(θ)=0 ?
The general solution for 2tan^2(θ)sin(θ)-tan^2(θ)=0 is θ=pin,θ= pi/6+2pin,θ=(5pi)/6+2pin