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

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

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

3 csc (2 x) + 2 = 0

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

Solution steps

3 csc (2 x) + 2 = 0

Move

2

to the right side

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

x, 2 cos^{2} (x) - 1 = 0

- 25 sin (5 x) = 0

6 sin^{2} (x) - sin (x) - 1 = 0

sin (x) = \frac{9}{11}

sec^{2} (x) = - 4

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