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

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

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sqrt(3)csc(x/2)-2=0

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

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

Solution steps

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

Move

2

to the right side

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

Divide both sides by

3

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

General solutions for

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

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

Solve

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

Solve

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

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

arcsin (y) = \frac{1}{2}

6 sin (y) = 0

tan (θ) = - \frac{3}{3}, 0 \leq θ \leq 2 π

cos (2 x) = sin (2 x) - 1

sinh^{2} (x) - 5 cosh (x) + 7 = 0

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