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

The general solution for csc^2(x)=2+csc(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin

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

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

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) = 2 + csc (x)

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{5.4}{1.1}

6 cos (2 θ) + 3 = 0

(sin (θ) + cos^{2} (θ))^{2} = 2 sin (θ)

\frac{2}{3} = sin (2 θ)

sin (3 x) - 2 = - 3 sin (3 x)

What is the general solution for csc^2(x)=2+csc(x) ?
The general solution for csc^2(x)=2+csc(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin