What is the general solution for 3csc^2(x)-5csc(x)=2 ?

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

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3csc^2(x)-5csc(x)=2

3 csc^{2} (x) - 5 csc (x) = 2

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

Solution steps

3 csc^{2} (x) - 5 csc (x) = 2

Solve by substitution

csc (x) = 2, csc (x) = - \frac{1}{3}

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

csc (x) = - \frac{1}{3} :

No Solution

Combine all the solutions

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

tan (2 x) - 3 tan (x) = 0

4 sin (x) - 3 cos (x) = 0

25 cos^{2} (3 x) + 10 cos (3 x) = 15

5 cos^{2} (x) = 6 sin (x)

sec^{2} (x) = 2 tan (x) + 4

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