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

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

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sqrt(3)csc(2x)=-2

3 csc (2 x) = - 2

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Solution steps

3 csc (2 x) = - 2

Divide both sides by

3

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

General solutions for

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

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

Solve

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

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

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

8 arctan (x) = 2 π

sin^{2} (θ) - 1 = cos^{2} (θ)

sin (\frac{1}{x}) = 0, 5

tan (2 x) sin (x) = sin (x)

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