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

cos (4 x) = \frac{- 1}{2}

2 cos (2 x) + sin (x) = 1

2 cos^{2} (x) - 3 cos (x) + 1 = 0, 0 \leq x \leq 2 π

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

2 sin^{2} (x) + 3 sin (x) + 1 = 0, 0 \leq x < 2 π

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