What is the general solution for sin^2(θ)-1/2 sin(θ)-1/2 =0 ?

The general solution for sin^2(θ)-1/2 sin(θ)-1/2 =0 is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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sin^2(θ)-1/2 sin(θ)-1/2 =0

sin^{2} (θ) - \frac{1}{2} sin (θ) - \frac{1}{2} = 0

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

sin^{2} (θ) - \frac{1}{2} sin (θ) - \frac{1}{2} = 0

Solve by substitution

sin (θ) = 1, sin (θ) = - \frac{1}{2}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

tan^{2} (x) - sec (x) + 1 = 0

sin (2 y) = 0

7 sin^{2} (θ) - 15 sin (θ) + 8 = 0

sin (5 t) = 0

cos (x) = 0, - π \leq x \leq π

What is the general solution for sin^2(θ)-1/2 sin(θ)-1/2 =0 ?
The general solution for sin^2(θ)-1/2 sin(θ)-1/2 =0 is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin