What is the general solution for 2sin^2(θ)+sqrt(3)sin(θ)=0 ?

The general solution for 2sin^2(θ)+sqrt(3)sin(θ)=0 is θ=2pin,θ=pi+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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2sin^2(θ)+sqrt(3)sin(θ)=0

2 sin^{2} (θ) + 3 sin (θ) = 0

θ = 2 πn, θ = π + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

2 sin^{2} (θ) + 3 sin (θ) = 0

Solve by substitution

sin (θ) = 0, sin (θ) = - \frac{3}{2}

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sin (θ) = - \frac{3}{2} : θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

cos^{2} (x) = sin^{2} (\frac{x}{2})

sin (x + \frac{π}{4}) = - \frac{2}{2}

1 = tan (θ)

2 cos (x) - 4 = 0

sec (x) = 1 - tan (x)

What is the general solution for 2sin^2(θ)+sqrt(3)sin(θ)=0 ?
The general solution for 2sin^2(θ)+sqrt(3)sin(θ)=0 is θ=2pin,θ=pi+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin