What is the general solution for csc^2(θ)+csc(θ)-2=0 ?

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

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csc^2(θ)+csc(θ)-2=0

csc^{2} (θ) + csc (θ) - 2 = 0

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

Solution steps

csc^{2} (θ) + csc (θ) - 2 = 0

Solve by substitution

csc (θ) = 1, csc (θ) = - 2

csc (θ) = 1 : θ = \frac{π}{2} + 2 πn

csc (θ) = - 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

2 sin (x) = cos (x)

2 + 2 sin (θ) = 4 cos^{2} (θ)

9 tan (x) sin (x) - 5 sin (x) = 0

x, y = arctan (x)

7 cos (x) + 7 sin (x) tan (x) = 14

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