What is the general solution for 2csc^2(x)-5csc(x)+2=0 ?

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

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2csc^2(x)-5csc(x)+2=0

2 csc^{2} (x) - 5 csc (x) + 2 = 0

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

Solution steps

2 csc^{2} (x) - 5 csc (x) + 2 = 0

Solve by substitution

csc (x) = 2, csc (x) = \frac{1}{2}

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

csc (x) = \frac{1}{2} :

No Solution

Combine all the solutions

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

x, sin (x) cos (x) = \frac{1}{2}

sec^{2} (x) + tan^{2} (x) = 1

csc (x) - 2 = 0

sin (θ) = - \frac{68}{9}

sec (θ) = 6

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