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

The general solution for sin^2(θ)=2*sin(θ)+3 is θ=(3pi)/2+2pin

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sin^2(θ)=2*sin(θ)+3

sin^{2} (θ) = 2 \cdot sin (θ) + 3

θ = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (θ) = 2 sin (θ) + 3

Solve by substitution

sin (θ) = 3, sin (θ) = - 1

sin (θ) = 3 :

No Solution

sin (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn

tan (3 x) = 1, - 2 π \leq x \leq 2 π

sin (x) = \frac{- 3}{2}

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

sin^{2} (x) = - cos (x)

arctan (x) = \frac{π}{12}

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