What is the general solution for csc^2(x)+csc(x)=2 ?

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

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csc^2(x)+csc(x)=2

csc^{2} (x) + csc (x) = 2

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

Solution steps

csc^{2} (x) + csc (x) = 2

Solve by substitution

csc (x) = 1, csc (x) = - 2

csc (x) = 1 : x = \frac{π}{2} + 2 πn

csc (x) = - 2 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

cos (t) = - 1

arccos (x) = 0

5 sin^{2} (x) - 1 = 0

sin^{2} (θ) = sin (θ) + 1 - sin^{2} (θ)

sin (x) = 0.75

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