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/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

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

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

tan (θ) = \frac{7}{4}

sin (x + 2 0^{\circ}) = cos (2 x + 2 5^{\circ})

- sin (x) - cos (2 x) = 0

cos (a) = \frac{1}{2}

sin (2 θ) - cos (2 θ) = 0

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/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin