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

The general solution for sqrt(3)csc^2(x)+2csc(x)=0 is x=(4pi)/3+2pin,x=(5pi)/3+2pin

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

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

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Solve by substitution

csc (x) = 0, csc (x) = - \frac{2 3}{3}

csc (x) = 0 :

No Solution

csc (x) = - \frac{2 3}{3} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

7 sin (2 x) sin (x) = 7 cos (x)

csc (x) + cot (x) = 3

sin^{2} (x) - sin (x) + 1 = cos^{2} (x)

sin (\frac{x}{2}) = \frac{3}{2}

cos (x) tan (x) - cos (x) = 0

What is the general solution for sqrt(3)csc^2(x)+2csc(x)=0 ?
The general solution for sqrt(3)csc^2(x)+2csc(x)=0 is x=(4pi)/3+2pin,x=(5pi)/3+2pin