What is the general solution for csc^2(x)-3csc(x)+2=0 ?

The general solution for csc^2(x)-3csc(x)+2=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin

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csc^2(x)-3csc(x)+2=0

csc^{2} (x) - 3 csc (x) + 2 = 0

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

Solution steps

csc^{2} (x) - 3 csc (x) + 2 = 0

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{π}{2} + 2 πn

Combine all the solutions

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

y, 5^{2 x} - sin (y) = x

sin^{2} (x) + 3 cos (x) = 3

3 tan (θ) = 0

2 sin (\frac{1}{2} x) - 1 = 0

sin (θ) = \frac{1}{3}, 0 < θ < \frac{π}{2}

What is the general solution for csc^2(x)-3csc(x)+2=0 ?
The general solution for csc^2(x)-3csc(x)+2=0 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin