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

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

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sqrt(3)sin(θ)-2sin^2(θ)=0

3 sin (θ) - 2 sin^{2} (θ) = 0

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

Solution steps

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

Combine all the solutions

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

3 tan (\frac{x}{3}) + 3 = 0

0 = 2 sin (2 x)

sec^{2} (x) = tan (x) + 1

x, cos (x) - sin (2 x) = 0

- \frac{2}{3} cos (3 θ) = 1, 0 \leq θ \leq 2 π

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