What is the general solution for sin^2(θ)= 1/2 ?

The general solution for sin^2(θ)= 1/2 is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin

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sin^2(θ)= 1/2

sin^{2} (θ) = \frac{1}{2}

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Solution steps

sin^{2} (θ) = \frac{1}{2}

Solve by substitution

sin (θ) = \frac{1}{2}, sin (θ) = - \frac{1}{2}

sin (θ) = \frac{1}{2} : θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

sin (θ) = - \frac{1}{2} : θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Combine all the solutions

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

1 + cos (θ) = 1 - sin (θ)

sin^{2} (x) - 2 sin (x) = 0

2 sin (x) = tan (x)

2 sin (θ) = - 1

1 - cos (x) = sin (x)

What is the general solution for sin^2(θ)= 1/2 ?
The general solution for sin^2(θ)= 1/2 is θ= pi/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin,θ=(7pi)/4+2pin